$$x = \dfrac{1}{4} \times 40 = 10$$ feet

Question 1

Which of the following is the correct graph of the equation $$y = 2x + 3$$?

Accepted Answer

A line passing through $$(0, 3)$$ with a slope of $$2.$$

Question 2

Find the $$x- $$and $$y-$$intercepts of the equation $$2x + 4y = 8.$$

Accepted Answer

$$x-$$intercept: $$(4, 0)$$; $$y-$$intercept: $$(0, 2)$$

Question 3

What is the slope of the line passing through the points $$(3, 4)$$ and $$(-2, -5)$$?

Accepted Answer

$$m = \dfrac{4 - (-5)}{3 - (-2)} = \dfrac{9}{5}$$

Question 4

Which equation represents a vertical line?

Accepted Answer

$$x = 2$$

Question 5

A company’s daily cost to manufacture $$x$$ bikes is given by $$y = 30x + 65. $$What is the cost to make $$10$$ bikes?

Accepted Answer

$$y = 30(10) + 65 = 365$$

Question 6

Joan makes $$300$$ per week plus $$12\%$$ commission on all sales. Which equation models her weekly income $$y in $$terms of sales $$x$$?

Accepted Answer

$$y = 0.12x + 300$$

Question 7

Given the line $$y = -\dfrac{2}{3}x + 4$$, what are the slope and $$y-$$intercept?

Accepted Answer

Slope: $$-\dfrac{2}{3}$$, $$y-$$intercept: $$4$$

Question 8

Find the equation of the line with slope $$-4$$ and $$y-$$intercept $$(0, 5).$$

Accepted Answer

$$y = -4x + 5$$

Question 9

A roof requires a pitch of $$\dfrac{1}{4}. If $$the roof measures $$40$$ feet from one side to the center, what is the required height $$x$$?

Accepted Answer

$$x = \dfrac{1}{4} 	imes 40 = 10$$ feet

Question 10

Which of the following lines is horizontal?

Accepted Answer

$$y = 6$$

Question 11

If a line passes through $$(2, 4)$$ and $$(x, 6)$$ and has a slope $$m = 2$$, what is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 12

Which of the following equations is in slope-intercept form?

Accepted Answer

$$y = mx + b$$

Question 13

Given the equation $$3x - 2y = 6$$, what is the slope of the line?

Accepted Answer

Slope $$= \dfrac{3}{-2} = -\dfrac{3}{2}$$

Question 14

If the equation of a line is $$y = 0$$, what kind of line is it?

Accepted Answer

A horizontal line passing through the origin

Question 15

A line passes through $$(0, -1)$$ and has a slope $$m = \dfrac{2}{3}. $$What is its equation?

Accepted Answer

$$y = \dfrac{2}{3}x - 1$$

Question 16

If the total cost to manufacture $$x$$ bikes is $$y = 30x + 65$$ and the total cost was $$605$$, how many bikes were made?

Accepted Answer

$$x = \dfrac{605 - 65}{30} = 18$$

Question 17

Which of the following best describes the slope of the line passing through $$(-2, 4)$$ and $$(-2, -6)$$?

Accepted Answer

Undefined

Question 18

Find the equation of the line with slope $$0$$ and $$y-$$intercept $$3.$$

Accepted Answer

$$y = 3$$

Question 19

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

Accepted Answer

$$0$$

Question 20

A line passes through $$(2, -3)$$ and has a slope of $$0. $$What is its equation?

Accepted Answer

$$y = -3$$

Guided Practice: Graphing, Slope, and Equations of Lines (Beginning & Intermediate Algebra)

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