Q: Which of the following pairs of lines are parallel?

$y = 3x + 1$ \,\text{and}\, y = 3x - 4$

Question 1

Which of the following is the correct definition of a linear function?

Accepted Answer

$f(x) = m 	imes x + b$

Question 2

Given the linear function $f(x) = 2x - 1$, what are the slope and y-intercept?

Accepted Answer

Slope $m = 2$, y-intercept $b = -1$

Question 3

A company models its profit with the equation $P(x) = 5x + 200$, where $x$ is the number of units sold. What does the slope represent in this context?

Accepted Answer

The profit per unit sold

Question 4

Given two points $(3, 7)$ and $(5, 15)$ on a line, what is the slope of the line?

Accepted Answer

$m = \frac{15 - 7}{5 - 3} = 4$

Question 5

Which of the following equations represents a horizontal line passing through the point $(1, 3)$?

Accepted Answer

$y = 3$

Question 6

If a line has the equation $y = -2x + 5$, what is the y-intercept?

Accepted Answer

$5$

Question 7

Which of the following pairs of lines are parallel?

Accepted Answer

$y = 3x + 1$ \,	ext{and}\, y = 3x - 4$

Question 8

Find the equation of the line passing through $(0, 3)$ and $(1, -1)$ in slope-intercept form.

Accepted Answer

$y = -4x + 3$

Question 9

A vertical line passes through the point $(1, 3)$. What is its equation?

Accepted Answer

$x = 1$

Question 10

Which of the following is the correct point-slope form for a line with slope $m = -5$ passing through $(-2, 7)$?

Accepted Answer

$y - 7 = -5(x + 2)$

Question 11

If a line is perpendicular to the line $y = \frac{1}{2}x + 3$, what is its slope?

Accepted Answer

$-2$

Question 12

Given the table below, which value of $f(x)$ is missing if the function is linear?

$x$: $-2$, $0$, $1$, $2$
$f(x)$: $3$, $0$, $-3$, $?$

Accepted Answer

$-6$

Question 13

A line contains the point $(0, 3)$ and is perpendicular to the line given by $x + 2y = 7$. What is the equation of the new line in slope-intercept form?

Accepted Answer

$y = \frac{1}{2}x + 3$

Question 14

Which of the following is NOT a possible application of linear equations?

Accepted Answer

Modeling exponential population growth

Question 15

Find the slope-intercept form of the line passing through $(-1, 6)$ and $(2, 12)$.

Question 16

If the equation of a line is $y = mx + b$ and $m = 0$, what type of line is this?

Accepted Answer

Horizontal line

Question 17

Given the line $y = 4x + 1$, what is the equation of a line perpendicular to it passing through $(0, 2)$?

Accepted Answer

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

Question 18

Which of the following statements is TRUE about the domain and range of a linear function $f(x) = mx + b$?

Accepted Answer

Domain is $(-\infty, \infty)$ and range is $(-\infty, \infty)$

Question 19

A line has the equation $x = 6$. What is the slope of this line?

Accepted Answer

Undefined

Question 20

Which of the following is the correct slope-intercept form for a line with slope $m = 2$ and y-intercept $b = -4$?

Accepted Answer

$y = 2x - 4$

Linear Functions and Equations of Lines: Precalculus Study Notes

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