Question 1

Given the points $$(4, 7)$$ and $$(8, 10)$$, what is the slope of the line passing through them, and does the line rise, fall, remain horizontal, or vertical?

Accepted Answer

$$m = \frac{3}{4}$$; the line rises from left to right.

Question 2

Which of the following best describes the slope and orientation of the line passing through the points $$(5, 3)$$ and $$(5, -2)$$?

Accepted Answer

The slope is undefined; the line is vertical.

Question 3

A road rises $$12$$ meters for every $$100$$ meters of horizontal distance. What is the slope of the road?

Accepted Answer

$$m = \frac{12}{100}$$

Question 4

Write the equation of the line in slope-intercept form that passes through $$(3, 5)$$ with a slope of $$2.$$

Accepted Answer

$$y = 2x - 1$$

Question 5

Which of the following is the point-slope form of the equation for a line with slope $$-3$$ passing through $$(-2, -3)$$?

Accepted Answer

$$y + 3 = -3(x + 2)$$

Question 6

A company’s profit $$P (in $$thousands of dollars) is a linear function of the number of units sold $$x. If $$the profit increases by $$4$$ thousand dollars for each additional unit sold and the company made $$3$$ thousand dollars profit when $$1$$ unit was sold, what is the equation for $$P in $$slope-intercept form?

Accepted Answer

$$P = 4x - 1$$

Question 7

Find the equation of the line in slope-intercept form that passes through $$(1, 2)$$ and $$(5, 10).$$

Accepted Answer

$$y = 2x$$

Question 8

A horizontal line passes through the point $$(4, -2). $$What is its equation?

Accepted Answer

$$y = -2$$

Question 9

Given the points $$(-3, 0)$$ and $$(0, 3)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 1$$

Question 10

A vertical line passes through the point $$(3, -4). $$What is its equation?

Accepted Answer

$$x = 3$$

Question 11

A biologist records the height of a plant every week. The data shows that the height increases by $$2 cm $$each week. If the plant was $$5 cm $$tall at week $$0$$, what is the equation for the height $$h (in cm) $$after $$w$$ weeks?

Accepted Answer

$$h = 2w + 5$$

Question 12

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

Accepted Answer

$$y = 2x$$

Question 13

Which of the following lines has a negative slope?

Accepted Answer

A line passing through $$(-3, 6)$$ and $$(3, -2)$$

Question 14

A line passes through $$(1, -3)$$ and has an $$x-$$intercept at $$-1. $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = x - 2$$

Question 15

If a line has a slope of $$0$$, which of the following statements is true?

Accepted Answer

The line is horizontal.

Question 16

A city’s water usage $$W (in $$thousands of gallons) is a linear function of the number of households $$h. If$$ $$W = 2h + 50$$, what is the slope and what does it represent?

Accepted Answer

Slope is $$2$$; each additional household uses $$2$$ thousand gallons.

Question 17

Given the points $$(6, -4)$$ and $$(4, -2)$$, what is the slope of the line passing through them?

Accepted Answer

$$m = 1$$

Question 18

Which of the following is the correct slope-intercept form for a line with slope $$6$$ passing through $$(-2, 5)$$?

Accepted Answer

$$y = 6x + 17$$

Question 19

A vertical flagpole casts a shadow that is always $$0$$ meters long at noon. What is the slope of the line representing the flagpole on a coordinate plane?

Accepted Answer

The slope is undefined.

Question 20

A line passes through the origin and has a slope of $$\frac{1}{2}. $$What is its equation in slope-intercept form?

Accepted Answer

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

Slope and Writing Linear Equations: Study Guide

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