Line $k$ is defined by $y=-\frac{17}{3}x+5$. Line $j$ is perpendicular to line $k$ in the xy-plane. What is the slope of line $j$?

The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is $\left(k-5,b\right)$, where $k$ and $b$ are constants. What is the value of $b$?

The total cost $f\left(x\right)$, in dollars, to lease a car for $36$ months from a particular car dealership is given by $f\left(x\right)=36x+\mathrm{1,000}$, where $x$ is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $\$400$?

$\frac{3}{2}y-\frac{1}{4}x=\frac{2}{3}-\frac{3}{2}y$

$\frac{1}{2}x+\frac{3}{2}=py+\frac{9}{2}$

In the given system of equations, $p$ is a constant. If the system has no solution, what is the value of $p$?

A window repair specialist charges $\$220$ for the first two hours of repair plus an hourly fee for each additional hour. The total cost for $5$ hours of repair is $\$400$. Which function $f$ gives the total cost, in dollars, for $x$ hours of repair, where $x\ge 2$?

The function $h$ is defined by $h\left(x\right)=4x+28$. The graph of $y=h\left(x\right)$ in the xy-plane has an x-intercept at $\left(a,0\right)$ and a y-intercept at $\left(0,b\right)$, where $a$ and $b$ are constants. What is the value of $a+b$?

For line $h$, the table shows three values of $x$ and their corresponding values of $y$. Line $k$ is the result of translating line $h$ down $5$ units in the xy-plane. What is the x-intercept of line $k$?

A certain apprentice has enrolled in $85$ hours of training courses. The equation $10x+15y=85$ represents this situation, where $x$ is the number of on-site training courses and $y$ is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

A store sells two different-sized containers of a certain Greek yogurt. The store’s sales of this Greek yogurt totaled $\mathrm{1,277.94}$ dollars last month. The equation $5.48x+7.30y=\mathrm{1,277.94}$ represents this situation, where $x$ is the number of smaller containers sold and $y$ is the number of larger containers sold. According to the equation, which of the following represents the price, in dollars, of each smaller container?

Line $k$ is defined by $y=3x+15$. Line $j$ is perpendicular to line $k$ in the xy-plane. What is the slope of line $j$?

The point $(8,2)$ in the xy-plane is a solution to which of the following systems of inequalities?

$5x=15$

$-4x+y=-2$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $x+y$?

The cost of renting a backhoe for up to $10$ days is $\$270$ for the first day and $\$135$ for each additional day. Which of the following equations gives the cost $y$, in dollars, of renting the backhoe for $x$ days, where $x$ is a positive integer and $x\le 10$?

What value of $p$ satisfies the equation $5p+180=250$?

The graph of a system of linear equations is shown. What is the solution $\left(x,y\right)$ to the system?

Line $p$ is defined by $4y+8x=6$. Line $r$ is perpendicular to line $p$ in the xy-plane. What is the slope of line $r$?

Line $p$ is defined by $2y+18x=9$. Line $r$ is perpendicular to line $p$ in the xy-plane. What is the slope of line $r$?

$d=16t$

The given equation represents the distance $d$, in inches, where $t$ represents the number of seconds since an object started moving. Which of the following is the best interpretation of $16$ in this context?

$f\left(x\right)=39$

For the given linear function $f$, which table gives three values of $x$ and their corresponding values of $f\left(x\right)$? 

The function $g$ is defined by $g\left(x\right)=6x$. For what value of $x$ is $g\left(x\right)=54$?

$4x+5=165$

What is the solution to the given equation?

A company that provides whale-watching tours takes groups of $21$ people at a time. The company’s revenue is $80$ dollars per adult and $60$ dollars per child. If the company’s revenue for one group consisting of adults and children was $\mathrm{1,440}$ dollars, how many people in the group were children?

In the xy-plane, the graph of the linear function $f$ contains the points $\left(0,3\right)$ and $\left(7,31\right)$. Which equation defines $f$, where $y=f\left(x\right)$?

The number $y$ is $84$ less than the number $x$. Which equation represents the relationship between $x$ and $y$?

The function $f$ is defined by the equation $f\left(x\right)=7x+2$. What is the value of $f\left(x\right)$ when $x=4$?

At how many points do the graphs of the equations $y=x+20$ and $y=8x$ intersect in the xy-plane?

John paid a total of $\$165$ for a microscope by making a down payment of $\$37$ plus $p$ monthly payments of $\$16$ each. Which of the following equations represents this situation?

$y=3x$

$2x+y=12$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $5x$?

$y=x+4$

Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

The total cost, in dollars, to rent a surfboard consists of a $\$25$ service fee and a $\$10$ per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $\$75$ to rent the surfboard. Which inequality represents this situation?

A model predicts that a certain animal weighed $241$ pounds when it was born and that the animal gained $3$ pounds per day in its first year of life. This model is defined by an equation in the form $f\left(x\right)=a+bx$, where $f\left(x\right)$ is the predicted weight, in pounds, of the animal $x$ days after it was born, and $a$ and $b$ are constants. What is the value of $a$?

What is the equation of the line that passes through the point $\left(0,5\right)$ and is parallel to the graph of $y=7x+4$ in the xy-plane?

$3x+21=3x+k$

In the given equation, $k$ is a constant. The equation has infinitely many solutions. What is the value of $k$?

Line $t$ in the xy-plane has a slope of $-\frac{1}{3}$ and passes through the point $\left(9,10\right)$. Which equation defines line $t$?

$2x+16=a\left(x+8\right)$

In the given equation, $a$ is a constant. If the equation has infinitely many solutions, what is the value of $a$?

If $\frac{x}{8}=5$, what is the value of $\frac{8}{x}$?

A machine makes large boxes or small boxes, one at a time, for a total of $700$ minutes each day. It takes the machine $10$ minutes to make a large box or $5$ minutes to make a small box. Which equation represents the possible number of large boxes, $x$, and small boxes, $y$, the machine can make each day?

The perimeter of an isosceles triangle is $83$ inches. Each of the two congruent sides of the triangle has a length of $24$ inches. What is the length, in inches, of the third side?

A total of $364$ paper straws of equal length were used to construct two types of polygons: triangles and rectangles. The triangles and rectangles were constructed so that no two polygons had a common side. The equation $3x+4y=364$ represents this situation, where $x$ is the number of triangles constructed and $y$ is the number of rectangles constructed. What is the best interpretation of $\left(x,y\right)=\left(24,73\right)$ in this context?

The function $f$ is defined by $f\left(x\right)=4x$. For what value of $x$ does $f\left(x\right)=8$?

On a car trip, Rhett and Jessica each drove for part of the trip, and the total distance they drove was under $220$ miles. Rhett drove at an average speed of $35 \text{miles} \text{per} \text{hour} \left(\text{mph}\right)$, and Jessica drove at an average speed of $40 \text{mph}$. Which of the following inequalities represents this situation, where $r$ is the number of hours Rhett drove and $j$ is the number of hours Jessica drove?

How many solutions does the equation $10\left(15x-9\right)=-15\left(6-10x\right)$ have?

$x+y=18$

$5y=x$

What is the solution $\left(x,y\right)$ to the given system of equations?

$y\le x+7$

$y\ge -2x-1$

Which point $\left(x,y\right)$ is a solution to the given system of inequalities in the xy-plane?

$y=2x+10$

$y=2x-1$

At how many points do the graphs of the given equations intersect in the xy-plane?

$4x-6y=10y+2$

$ty=\frac{1}{2}+2x$

In the given system of equations, $t$ is a constant. If the system has no solution, what is the value of $t$?

An employee at a restaurant prepares sandwiches and salads. It takes the employee $1.5$ minutes to prepare a sandwich and $1.9$ minutes to prepare a salad. The employee spends a total of $46.1$ minutes preparing $x$ sandwiches and $y$ salads. Which equation represents this situation?

$F\left(x\right)=\frac{9}{5}\left(x-273.15\right)+32$

The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $9.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?

$3(kx+13)=\frac{48}{17}x+36$

In the given equation, $k$ is a constant. The equation has no solution. What is the value of $k$?

The function $f$ is defined by $f\left(x\right)=7x-84$. What is the x-intercept of the graph of $y=f\left(x\right)$ in the xy-plane?

The table shows four values of $x$ and their corresponding values of $f\left(x\right)$. There is a linear relationship between $x$ and $f\left(x\right)$ that is defined by the equation $f\left(x\right)=mx-28$, where $m$ is a constant. What is the value of $m$?

$x=10$

$y=x+21$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $y$?

$y=-\frac{1}{9}x$

$y=\frac{1}{2}x$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $x$?

A salesperson’s total earnings consist of a base salary of $x$ dollars per year, plus commission earnings of $11\%$ of the total sales the salesperson makes during the year. This year, the salesperson has a goal for the total earnings to be at least $3$ times and at most $4$ times the base salary. Which of the following inequalities represents all possible values of total sales $s$, in dollars, the salesperson can make this year in order to meet that goal? 

The graph of the function $f$, where $y=f(x)$, gives the total cost $y$, in dollars, for a certain video game system and $x$ games. What is the best interpretation of the slope of the graph in this context?

A bus traveled on the highway and on local roads to complete a trip of $160 \text{miles}$. The trip took $4 \text{hours}$. The bus traveled at an average speed of $55 \text{miles} \text{per} \text{hour} \left(\text{mph}\right)$ on the highway and an average speed of $25 \text{mph}$ on local roads. If $x$ is the time, in hours, the bus traveled on the highway and $y$ is the time, in hours, it traveled on local roads, which system of equations represents this situation?

Ty set a goal to walk at least $24$ kilometers every day to prepare for a multiday hike. On a certain day, Ty plans to walk at an average speed of $4$ kilometers per hour. What is the minimum number of hours Ty must walk on that day to fulfill the daily goal?

The functions $f$ and $g$ are defined as $f\left(x\right)=\frac{1}{4}x-9$ and $g\left(x\right)=\frac{3}{4}x+21$. If the function $h$ is defined as $h\left(x\right)=f\left(x\right)+g\left(x\right)$, what is the x-coordinate of the x-intercept of the graph of $y=h\left(x\right)$ in the xy-plane?

A principal used a total of $25$ flags that were either blue or yellow for field day. The principal used $20$ blue flags. How many yellow flags were used?

$x+3=-2y+5$

$x-3=2y+7$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $2x$?

$8x=88$

What value of $x$ is the solution to the given equation?

The graph shown models the number of candy bars a certain machine wraps with a label in $x$ seconds.

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

A number $x$ is at most $2$ less than $3$ times the value of $y$. If the value of $y$ is $-4$, what is the greatest possible value of $x$?

Caleb used juice to make popsicles. The function $f\left(x\right)=-5x+30$ approximates the volume, in fluid ounces, of juice Caleb had remaining after making $x$ popsicles. Which statement is the best interpretation of the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane in this context?

In the xy-plane, the graph of the linear function $f$ contains the points $\left(0,2\right)$ and $\left(8,34\right)$. Which equation defines $f$, where $y=f\left(x\right)$?

The y-intercept of the graph of $12x+2y=18$ in the xy-plane is $\left(0,y\right)$. What is the value of $y$?

In the xy-plane, line $\mathcal{l}$ passes through the point $\left(0,0\right)$ and is parallel to the line represented by the equation $y=8x+2$. If line $\mathcal{l}$ also passes through the point $\left(3,d\right)$, what is the value of $d$?

Sean rents a tent at a cost of $\$11$ per day plus a onetime insurance fee of $\$10$. Which equation represents the total cost $c$, in dollars, to rent the tent with insurance for $d$ days?

The graph of $y=f\left(x\right)+14$ is shown. Which equation defines function $f$?

Keenan made $32$ cups of vegetable broth. Keenan then filled $x$ small jars and $y$ large jars with all the vegetable broth he made. The equation $3x+5y=32$ represents this situation. Which is the best interpretation of $5y$ in this context?

$y<-4x+4$

Which point ($x$, $y$) is a solution to the given inequality in the $xy$-plane?

The graph shows the possible combinations of the number of pounds of tangerines and lemons that could be purchased for $\$18$ at a certain store. If Melvin purchased lemons and $4$ pounds of tangerines for a total of $\$18$, how many pounds of lemons did he purchase?

A bus is traveling at a constant speed along a straight portion of road. The equation $d=30t$ gives the distance $d$, in feet from a road marker, that the bus will be $t$ seconds after passing the marker. How many feet from the marker will the bus be $2$ seconds after passing the marker?

$y=4x+1$
$4y=15x-8$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $x-y$?

The cost $y$, in dollars, for a manufacturer to make $x$ rings is represented by the line shown.

What is the cost, in dollars, for the manufacturer to make $60$ rings?

$3$ more than $8$ times a number $x$ is equal to $83$. Which equation represents this situation?

What is an equation of the graph shown?

$4x=20$

$-3x+y=-7$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $x+y$?

$4x+6=18$

Which equation has the same solution as the given equation?

The function $h$ is defined by $h\left(x\right)=3x-7$. What is the value of $h\left(-2\right)$?

$2\left(kx-n\right)=-\frac{28}{15}x-\frac{36}{19}$

In the given equation, $k$ and $n$ are constants and $n>1$. The equation has no solution. What is the value of $k$?

$y=-4x+40$

Which table gives three values of $x$ and their corresponding values of $y$ for the given equation?

For the linear function $f$, the table shows three values of $x$ and their corresponding values of $f\left(x\right)$. Which equation defines $f\left(x\right)$?

A small business owner budgets $\$\mathrm{2,200}$ to purchase candles. The owner must purchase a minimum of $200$ candles to maintain the discounted pricing. If the owner pays $\$4.90$ per candle to purchase small candles and $\$11.60$ per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

A number $x$ is at most $17$ less than $5$ times the value of $y$. If the value of $y$ is $3$, what is the greatest possible value of $x$?

The graph of $7x+2y=-31$ in the $xy$-plane has an $x$-intercept at $(a,0)$ and a $y$-intercept at $(0,b)$, where $a$ and $b$ are constants. What is the value of $\frac{b}{a}$?

Nasir bought $9$ storage bins that were each the same price. He used a coupon for $\text{\$}63$ off the entire purchase. The cost for the entire purchase after using the coupon was $\text{\$}27$. What was the original price, in dollars, for $1$ storage bin?

The graph shows the relationship between the number of shares of stock from Company A, $x$, and the number of shares of stock from Company B, $y$, that Simone can purchase. Which equation could represent this relationship?

$48x-72y=30y+24$

$ry=\frac{1}{6}-16x$

In the given system of equations, $r$ is a constant. If the system has no solution, what is the value of $r$?

For a training program, Juan rides his bike at an average rate of $5.7$ minutes per mile. Which function $m$ models the number of minutes it will take Juan to ride $x$ miles at this rate?

For the linear function $f$, the table shows three values of $x$ and their corresponding values of $f\left(x\right)$. Function $f$ is defined by $f\left(x\right)=ax+b$, where $a$ and $b$ are constants. What is the value of $a-b$?

$x+40=95$

What value of $x$ is the solution to the given equation?

$y=4x-9$
$y=19$

What is the solution $\left(x,y\right)$ to the given system of equations?

$24x+y=48$

$6x+y=72$

The solution to the given system of equations is $(x,y)$. What is the value of $y$?

If $2x=12$, what is the value of $9x$?

$5(t+3)-7(t+3)=38$

What value of $t$ is the solution to the given equation?

One gallon of paint will cover $220$ square feet of a surface. A room has a total wall area of $w$ square feet. Which equation represents the total amount of paint $P$, in gallons, needed to paint the walls of the room twice?

For the function $f$, the graph of $y=f\left(x\right)$ in the xy-plane has a slope of $3$ and passes through the point $\left(0,-8\right)$. Which equation defines $f$?

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. If a triangle has side lengths of $6$ and $12$, which inequality represents the possible lengths, $x$, of the third side of the triangle?

If $5\left(x+4\right)=4\left(x+4\right)+29$, what is the value of $x+4$?

The equation $40x+20y=160$ represents the number of sweaters, $x$, and number of shirts, $y$, that Yesenia purchased for $\$160$. If Yesenia purchased $2$ sweaters, how many shirts did she purchase?  

If $x=7$, what is the value of $x+20$?

A gym charges its members a onetime $\$36$ enrollment fee and a membership fee of $\$19$ per month. If there are no charges other than the enrollment fee and the membership fee, after how many months will a member have been charged a total of $\$188$ at the gym?

If $7x=28$, what is the value of $8x$?

$x+2y=6$

$x-2y=4$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $x$?

If $4x+2=12$, what is the value of $16x+8$?

A linear model estimates the population of a city from $1991$ to $2015$. The model estimates the population was $57$ thousand in $1991$, $224$ thousand in $2011$, and $x$ thousand in $2015$. To the nearest whole number, what is the value of $x$?

The table shows three values of $x$ and their corresponding values of $y$. There is a linear relationship between $x$ and $y$. Which of the following equations represents this relationship?

The shaded region shown represents solutions to an inequality. Which ordered pair $\left(x,y\right)$ is a solution to this inequality?

In the linear function $f$, $f\left(0\right)=8$ and $f\left(1\right)=12$. Which equation defines $f$?

$f\left(x\right)=2x+244$

The given function $f$ represents the perimeter, in $\text{centimeters} \left(\text{cm}\right)$, of a rectangle with a length of $x \text{cm}$ and a fixed width. What is the width, in $\text{cm}$, of the rectangle?

$-15x+25y=65$

One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?

$x=5$

$y=x-8$

Which of the following points $\left(x,y\right)$ is the solution to the given system of equations in the xy-plane?

$w\left(t\right)=300-4t$

The function $w$ models the volume of liquid, in milliliters, in a container $t$ seconds after it begins draining from a hole at the bottom. According to the model, what is the predicted volume, in milliliters, draining from the container each second?

If $6+x=9$, what is the value of $18+3x$?

$y>14$

$4x+y<18$

The point $\left(x,53\right)$ is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of $x$?

$3x=12$

$-3x+y=-6$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $y$?

$F\left(x\right)=\frac{9}{5}\left(x-273.15\right)+32$

The function $F$ gives the temperature, in degrees Fahrenheit, that corresponds to a temperature of $x$ kelvins. If a temperature increased by $2.10$ kelvins, by how much did the temperature increase, in degrees Fahrenheit?

$s=40+3t$

The equation gives the speed $s$, in miles per hour, of a certain car $t$ seconds after it began to accelerate. What is the speed, in miles per hour, of the car $5$ seconds after it began to accelerate?

Each side of a $30$-sided polygon has one of three lengths. The number of sides with length $8 \text{centimeters} \left(\text{cm}\right)$ is $5$ times the number of sides $n$ with length $3 \text{cm}$. There are $6$ sides with length $4 \text{cm}$. Which equation must be true for the value of $n$?

Connor has $c$ dollars and Maria has $m$ dollars. Connor has $4$ times as many dollars as Maria, and together they have a total of $\$25.00$. Which system of equations represents this situation?

$j\left(x\right)=mx+144$

For the linear function $j$, $m$ is a constant and $j\left(12\right)=18$. What is the value of $j\left(10\right)$?

$y<6x+2$

For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?

The table gives the number of hours, $h$, of labor and a plumber’s total charge $f\left(h\right)$, in dollars, for two different jobs.

There is a linear relationship between $h$ and $f\left(h\right)$. Which equation represents this relationship?

A wire with a length of $106$ inches is cut into two parts. One part has a length of $x$ inches, and the other part has a length of $y$ inches. The value of $x$ is $6$ more than $4$ times the value of $y$. What is the value of $x$?

$y>13x-18$

For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given inequality?

$5x+14y=45$

$10x+7y=27$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of $xy$?

The graph of $9x-10y=19$ is translated down $4$ units in the xy-plane. What is the x-coordinate of the x-intercept of the resulting graph?

$-3x+21px=84$

In the given equation, $p$ is a constant. The equation has no solution. What is the value of $p$?

$6x+7y=28$
$2x+2y=10$

The solution to the given system of equations is $\left(x,y\right)$. What is the value of y?

When line $n$ is graphed in the xy-plane, it has an x-intercept of $\left(-4,0\right)$ and a y-intercept of $\left(0,\frac{86}{3}\right)$. What is the slope of line $n$?

The function $f$ is defined by $f\left(x\right)=\frac{x+15}{5}$, and $f\left(a\right)=10$, where $a$ is a constant. What is the value of $a$?

If $2(3t-10)+t=40+4t$, what is the value of $3t$?

If $\frac{x+6}{3}=\frac{x+6}{13}$, the value of $x+6$ is between which of the following pairs of values?

In the xy-plane, line $k$ passes through the points $\left(0,-5\right)$ and $\left(1,-1\right)$. Which equation defines line $k$?

The function $f$ is defined by the equation $f\left(x\right)=100x+2$. What is the value of $f\left(x\right)$ when $x=9$?

A line in the xy-plane has a slope of $\frac{1}{9}$ and passes through the point $\left(0,14\right)$. Which equation represents this line?

Vivian bought party hats and cupcakes for $\$71$. Each package of party hats cost $\$3$, and each cupcake cost $\$1$. If Vivian bought $10$ packages of party hats, how many cupcakes did she buy?