SAT Prep Plus 2021

Kaplan Test Prep

Chapter 4

Linear Equations and Graphs

Educators

Chapter Questions

Problem 1

Which value of $x$ makes the equation $\frac{8}{5}\left(x+\frac{33}{12}\right)=16$ true?
a.7.25
b.8.75
c.12.75
d.13.25

James K.

James K.

Numerade Educator

Problem 2

The graph above shows the cost of joining and buying music from a music subscription service. What does the $y$ -intercept of the line most likely represent?
a.The cost per song
b.The cost to join the service
c.The cost of buying 20 songs
d.The cost of 20 subscriptions to the service

James K.

Numerade Educator

Problem 3

If $\frac{3}{4} y=6-\frac{1}{3} c,$ then what is the value of $2 c+\frac{9}{2} y ?$

James K.

Numerade Educator

Problem 4

Three years ago, Madison High School started charging an admission fee for basketball games to raise money for new bleachers. The initial price was $\$ 2$ per person; the school raised the price of admission to $\$ 2.50$ this year. Assuming this trend continues, which of the following equations can be used to describe $c,$ the cost of admission, $y$ years after the school began charging for admission to games?
a.$c = 6 y+2$
b.$c = \frac{y}{6}+2.5$
c.$c$ = $\frac{y}{6}+2$
d.$c =\frac{y}{2}+2$

James K.

Numerade Educator

Problem 5

Which of the following equations best describes the linear relationship shown in the table, where $g$ represents the number of pounds of grain sold and $d$ represents the price in dollars of one pound of grain?
a.$g = 1.2 d+12,500$
b.$g = 12,500 d+15,000$
c.$g$ = $-12,500 d+17,500$
d.$g$ =$-12,500 d+30,000$

James K.

Numerade Educator

Problem 6

Brian and Jared live in the same apartment complex and both bike to and from work every day. The figure above shows a typical commute home for each of them. Based on the figure, which of the following statements is true?
a.It takes Brian longer to bike home because his work is farther away.
b.It takes Jared longer to bike home because his work is farther away.
c.Jared and Brian arrive home at the same time, so they must bike at about the same rate.
d.Jared bikes a longer distance than Brian in the same amount of time, so Jared must bike at a faster rate.

James K.

Numerade Educator

Problem 7

When graphing a linear equation that is written in the form $y=m x+b$, the variable $m$ represents the slope of the line and $b$ represents the $y$ - intercept. Assuming that $b>0,$ which of the following best describes how reversing the sign of $b$ will affect the graph?
a.The new line will be shifted down $b$ units.
b.The new line will be shifted down $2 b$ units.
c.The new line will be shifted down $2 b$ units.
d.The new line will be a perfect reflection across the $y$ -axis.

James K.

Numerade Educator

Problem 8

The graph of a line in the $x y$ -plane passes through the points (5,4) and $\left(3, \frac{1}{2}\right) \cdot$ Which of the following equations describes the line?
a.$y=\frac{7}{4} x+\frac{19}{4}$
b.$y=-\frac{7}{4} x-\frac{19}{4}$
c.$y=\frac{7}{4} x-\frac{19}{4}$
d.$y=\frac{4}{7} x+\frac{8}{7}$

James K.

Numerade Educator

Problem 9

Line $f$ in the $x y$ -plane passes through the origin and has a slope of $-\frac{2}{5}$. Line $z$ is perpendicular to line $f$ and passes through the point $(6,2) .$ Which of the following is the equation of line $z ?$
a.$y=-\frac{2}{5} x$
b.$y=-\frac{2}{5} x-13$
c.$y=\frac{5}{2} x$
d.$y=\frac{5}{2} x-13$

James K.

Numerade Educator

Problem 10

A circle of rubber with a constant diameter $d$ is placed on a table; its perimeter is anchored to the table and a string is attached to its center. When the string is pulled upwards, a cone is formed with height $h$ and volume $V$. The relationship between $d, h,$ and $V$ is represented above. Which of the following statements must be true?
As the volume of the cone decreases, the height also decreases.
If the diameter of the base of the cone is 6 centimeters, the height can be determined by dividing the volume by $3 \pi$.
If the height of the cone triples, the volume must also triple.
I only
I and II only
II and III only
I,II, and III

James K.

Numerade Educator

Problem 11

If the height of the cone triples, the volume must also triple.
I only
I and II only
II and III only
I,II, and III

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