Question 1

A business analyst is studying the relationship between advertising spending and sales. She finds that for every $1,000 increase in advertising, sales increase by $2,500. If the relationship is linear and the y-intercept is $10,000, which equation best models this scenario?

Accepted Answer

$y = 2,500x + 10,000$

Question 2

Given the points $(4, -3)$ and $(4, 5)$, what is the slope of the line passing through them?

Accepted Answer

$m$ is undefined

Question 3

Which of the following is the point-slope form of the equation for a line passing through $(6, 3)$ with slope $7$?

Accepted Answer

$y - 3 = 7(x - 6)$

Question 4

A city planner wants to design a road perpendicular to an existing road with equation $y = -\frac{2}{3}x + 5$. What should be the slope of the new road?

Accepted Answer

$\frac{3}{2}$

Question 5

Which of the following equations represents a vertical line passing through $x = -4$?

Accepted Answer

$x = -4$

Question 6

Find the slope-intercept form of the line passing through $(-5, 4)$ and $(5, 2)$.

Accepted Answer

$y = -\frac{1}{5}x + 3$

Question 7

Which of the following statements is true about parallel lines in the plane?

Accepted Answer

Parallel lines have equal slopes.

Question 8

A psychologist models the relationship between stress level $y$ and hours of sleep $x$ as $y = -2x + 16$. What is the slope and what does it represent?

Accepted Answer

Slope is $-2$; each additional hour of sleep reduces stress by 2 units.

Question 9

Which of the following is the general form of a line with slope $1$ passing through $(-5, -1)$?

Accepted Answer

$-x + y - 4 = 0$

Question 10

A horizontal line passes through the point $(0, 6)$. What is its equation?

Accepted Answer

$y = 6$

Question 11

A line passes through $(2, -3)$ and is parallel to $4x + 5y = 10$. What is its equation in point-slope form?

Accepted Answer

$y + 3 = -\frac{4}{5}(x - 2)$

Question 12

If a line has slope $m$, what is the slope of a line perpendicular to it?

Accepted Answer

$-\frac{1}{m}$

Question 13

A medical researcher finds that the recovery time $y$ (in days) decreases by 3 days for every additional hour of physical therapy $x$. If the y-intercept is 20, what is the equation for recovery time?

Accepted Answer

$y = -3x + 20$

Question 14

Which of the following is the correct slope-intercept form for a line with slope $-4$ and y-intercept $6$?

Accepted Answer

$y = -4x + 6$

Question 15

Given the line $2x - y = 1$, what is the slope of a line perpendicular to it?

Accepted Answer

$-\frac{1}{2}$

Question 16

A line passes through $(1, 7)$ and is perpendicular to $y = 3x - 4$. What is its equation in point-slope form?

Accepted Answer

$y - 7 = -\frac{1}{3}(x - 1)$

Question 17

Which of the following is NOT a possible form for the equation of a line?

Accepted Answer

$y = mx^2 + b$

Question 18

A line passes through $(9, 3)$ with slope $-1$. What is its equation in point-slope form?

Accepted Answer

$y - 3 = -1(x - 9)$

Question 19

Which of the following best describes the slope of a horizontal line?

Accepted Answer

The slope is $0$.

Lines in the Plane: Slope, Equations, and Relationships

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