Question 1

Given the equation $y = mx + b$, what does the parameter $m$ represent in the context of a real-world scenario, such as Sonya walking away from home at a constant speed?

Accepted Answer

The rate at which Sonya is walking away from home

Question 2

Sonya is 10 miles from home and walks away at 2 miles per hour. Which equation models her distance from home $t$ hours from now?

Accepted Answer

$y = 2t + 10$

Question 3

A boat is 100 miles from the marina, sailing directly toward it at 10 miles per hour. What is the equation for its distance from the marina after $t$ hours?

Accepted Answer

$y = 100 - 10t$

Question 4

Which of the following equations represents a line with a negative slope and a $y$-intercept of $-4$?

Accepted Answer

$f(x) = -x - 4$

Question 5

Given the two functions $f(x) = 5x - 1$ and $g(x) = 6 - x$, at what $x$-value do they intersect?

Accepted Answer

$x = 1.17$

Question 6

What is the $y$-intercept of the line $y = -2x + 2$?

Accepted Answer

$2$

Question 7

Which equation matches a line that passes through the point $(0, 1)$ and has a slope of $3$?

Accepted Answer

$y = 3x + 1$

Question 8

If a line has the equation $y = 3x - \frac{1}{3}$, what is its slope?

Accepted Answer

$3$

Question 9

Which of the following equations represents a line parallel to $y = 3x + 1$?

Accepted Answer

$y = 3x - 4$

Question 10

Given the system of equations $7x + 2y = -1$ and $21x + 6y = -3$, what can you conclude about the system?

Accepted Answer

The system has infinitely many solutions

Question 11

Which transformation occurs when the equation $y = x$ is changed to $y = x + 2$?

Accepted Answer

A vertical shift up by 2 units

Question 12

If the equation of a line is $y = -\frac{1}{3}x$, what is the $y$-intercept?

Accepted Answer

$0$

Question 13

Which equation represents a line with a slope of $\frac{1}{3}$ and a $y$-intercept of $2$?

Accepted Answer

$f(x) = \frac{1}{3}x + 2$

Question 14

Given the system $-4x + y = 5$ and $8x - 2y = 3$, what is the solution for $x$?

Accepted Answer

$x = -1$

Question 15

Which of the following best describes the slope of the line $y = -2x + 2$?

Accepted Answer

The line decreases by 2 units in $y$ for every 1 unit increase in $x$

Question 16

If two lines have the same slope but different $y$-intercepts, what is true about their graphs?

Accepted Answer

They are parallel and never intersect

Question 17

Which equation represents a line perpendicular to $y = x$?

Accepted Answer

$y = -x$

Question 18

A line passes through $(0, -4)$ and has a slope of $-3$. What is its equation?

Accepted Answer

$y = -3x - 4$

Question 19

If the equation of a line is $y = 3x + 1$, what is the value of $y$ when $x = 2$?

Accepted Answer

$y = 7$

Question 20

Which of the following equations has a slope of $-2$ and a $y$-intercept of $2$?

Accepted Answer

$y = -2x + 2$

Linear Functions, Graphs, and Systems of Equations: Precalculus Study Notes

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