Question 1

A road construction company is designing a ramp that rises 4 feet for every 15 feet of horizontal distance. What is the slope of the ramp?

Accepted Answer

$$\frac{4}{15}$$

Question 2

Which of the following equations represents a line parallel to $$y = -3x + 2$$?

Accepted Answer

$$y = -3x - 5$$

Question 3

A biologist tracks the growth of a plant and finds that its height increases by 2.5 cm every week. If the initial height is 10 cm, which equation models the plant's height $$h (in cm) $$after $$w$$ weeks?

Accepted Answer

$$h = 2.5w + 10$$

Question 4

Given the points $$A(-2, 5)$$ and $$B(4, -1)$$, what is the slope of the line passing through these points?

Accepted Answer

$$-1$$

Question 5

A vertical line passes through the point $$(3, -2). $$What is its equation?

Accepted Answer

$$x = 3$$

Question 6

A line has a slope of $$\frac{1}{5}$$ and passes through the point $$(0, 7). $$What is its $$y-$$intercept?

Accepted Answer

$$7$$

Question 7

Which of the following statements is true about the line $$y = 4x - 6$$?

Accepted Answer

The slope is $$4$$ and the $$y-$$intercept is $$-6.$$

Question 8

A chemist plots the temperature of a solution over time and finds the equation $$T = -2t + 100$$, where $$T is $$temperature in degrees Celsius and $$t is $$time in minutes. What does the slope represent?

Accepted Answer

The temperature decreases by $$2$$ degrees Celsius per minute.

Question 9

Find the equation of the line in slope-intercept form that passes through $$(-3, -4)$$ and $$(2, 4).$$

Accepted Answer

$$y = \frac{8}{5}x + \frac{4}{5}$$

Question 10

A line has the equation $$y = \frac{11x - 13}{4x}. $$What is the slope of this line?

Accepted Answer

$$\frac{11}{4}$$

Question 11

Which of the following is the equation of a line with slope $$-4$$ and $$y-$$intercept $$9$$?

Accepted Answer

$$y = -4x + 9$$

Question 12

A line passes through the point $$(0, 3)$$ and has a slope of $$\frac{1}{3}. $$What is its equation in slope-intercept form?

Accepted Answer

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

Question 13

A line has $$x-$$intercept $$-2$$ and $$y-$$intercept $$8. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 4x + 8$$

Question 14

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

Accepted Answer

$$0$$

Question 15

A line has the equation $$y = mx + b. If$$ $$m = 0$$, what kind of line is this?

Accepted Answer

A horizontal line

Question 16

A line passes through $$(1, 2)$$ and has a slope of $$-3. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -3x + 5$$

Question 17

A medical researcher records a patient's blood pressure every hour. The data fits the equation $$P = 120 - 2t$$, where $$P is $$the blood pressure and $$t is $$time in hours. What is the patient's blood pressure after 5 hours?

Accepted Answer

$$110$$

Question 18

Which of the following lines is perpendicular to $$y = \frac{1}{2}x + 3$$?

Accepted Answer

$$y = -2x + 1$$

Question 19

A line has a slope of $$\frac{3}{4}$$ and passes through $$(0, -2). $$What is its $$y-$$intercept?

Accepted Answer

$$-2$$

Question 20

A line passes through $$(2, 5)$$ and $$(6, 1). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -x + 7$$

Linear Equations and Slope: Precalculus Study Notes

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