Question 1

What are the x- and y-intercepts of the equation $3x + 5y = 30$?

Accepted Answer

x-intercept: $x = 10$, y-intercept: $y = 6$

Question 2

What is the slope of the line passing through the points $(2,1)$ and $(8,4)$?

Accepted Answer

$\frac{1}{6}$

Question 3

Find the equation of the line in slope-intercept form that passes through $(-3,7)$ and $(1,11)$.

Accepted Answer

$y = x + 4$

Question 4

Which of the following is the equation of a horizontal line through $(2,5)$?

Accepted Answer

$y = 5$

Question 5

Given the function $q(x) = \frac{2x-3}{x+1}$, what is $q(4)$?

Accepted Answer

$1$

Question 6

For the function $q(x) = \frac{2x-3}{x+1}$, what is the domain?

Accepted Answer

All real numbers except $x = -1$

Question 7

A granola mix contains 25% dried fruit, and another contains 10% dried fruit. How many pounds of each should be mixed to get 20 lbs of a 19% dried fruit mix?

Accepted Answer

12 lbs of 25% mix, 8 lbs of 10% mix

Question 8

Solve the system: $\begin{cases} x - y = 8 \ y = 5x \end{cases}$

Accepted Answer

$x = 2, y = 10$

Question 9

A clothing store sold 36 sweatshirts yesterday. White sweatshirts cost $10.95 and yellow ones cost $13.50. If the total sales were $435, how many of each were sold?

Accepted Answer

21 white, 15 yellow

Question 10

Given the piecewise function $g(x) = \begin{cases} x^2 & x \leq 2 \ -2 & x > 2 \end{cases}$, what is $g(3)$?

Accepted Answer

$-2$

Question 11

What is the equation of the line in slope-intercept form passing through $(4,6)$ and $(0,-2)$?

Accepted Answer

$y = 2x - 2$

Question 12

If $f(x)$ is the function graphed as a downward opening parabola with vertex at $(1,5)$ and $f(x) = -x^2 + 2x + 4$, for what values of $x$ does $f(x) = 5$?

Accepted Answer

$x = -1$ and $x = 3$

Question 13

Given the system $\begin{cases} 9x + 2y = 7 \ x - 6y = 7 \end{cases}$, what is the solution $(x, y)$?

Question 14

What is the equation of the line with slope $\frac{3}{5}$ passing through $(1,2)$?

Accepted Answer

$y = \frac{3}{5}x + \frac{7}{5}$

Question 15

For the function $g(x) = \begin{cases} x^2 & x \leq 2 \ -2 & x > 2 \end{cases}$, what is the range?

Accepted Answer

$(-\infty, 4] \cup \{-2\}$

Question 16

If a line passes through $(2,5)$ and has a slope of $-3$, what is its equation in slope-intercept form?

Accepted Answer

$y = -3x + 11$

Question 17

Solve the system: $\begin{cases} 2x + 5y = 18 \ 4x + y = 9 \end{cases}$

Accepted Answer

$x = 1, y = 2$

Question 18

Which of the following best describes the domain of the function $f(x) = \frac{2x-3}{x+1}$?

Accepted Answer

$(-\infty, -1) \cup (-1, \infty)$

Question 19

If a line passes through $(4,6)$ and $(-6,3)$, what is its slope?

College Algebra Study Guide: Linear Equations, Functions, and Systems

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