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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