Question 1

Given two points $$A(-2, -3)$$ and $$B(1, 3)$$, what is the equation of the line passing through these points in point-slope form?

Accepted Answer

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

Question 2

Which of the following is the slope-intercept form of the line passing through the points $$(-2, 1)$$ and $$(2, 3)$$?

Accepted Answer

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

Question 3

What is the standard form of a line?

Accepted Answer

$$Ax + By = C$$

Question 4

Find the $$x- $$and $$y-$$intercepts of the line $$4x + 3y = 6.$$

Accepted Answer

$$x-$$intercept: $$(1.5, 0)$$, $$y-$$intercept: $$(0, 2)$$

Question 5

Which equation represents a horizontal line with $$y-$$intercept $$b$$?

Accepted Answer

$$y = b$$

Question 6

Which equation represents a vertical line passing through $$x = 3$$?

Accepted Answer

$$x = 3$$

Question 7

A company’s sales decreased from 55 million units in 2008 to 43 million units in 2011. What is the slope of the line modeling this data, and what does it represent?

Accepted Answer

$$m = -4$$, representing a decrease of 4 million units per year

Question 8

If you use a linear model based on data from 2008 and 2011 to estimate sales in 2010, what type of prediction is this?

Accepted Answer

Interpolation

Question 9

Given the line $$3x + 4y = 12$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 3)$$

Question 10

Which of the following best describes the accuracy of interpolation versus extrapolation?

Accepted Answer

Interpolation is usually more accurate than extrapolation.

Question 11

A linear model for global car shipments is $$y = \frac{19}{6}(x - 2013) + 69. $$What does the slope represent?

Accepted Answer

Shipments increased by about 3.17 million per year between 2013 and 2019.

Question 12

Which of the following is the equation of a line in standard form that is horizontal?

Accepted Answer

$$0x + 1y = 2$$

Question 13

If a line has an undefined slope, which of the following must be true?

Accepted Answer

The line is vertical.

Question 14

Given the equation $$y = -4(x - 2008) + 55$$, what is the estimated value of $$y$$ when $$x = 2010$$?

Accepted Answer

$$47$$

Question 15

Which of the following is NOT a valid equation for a line?

Accepted Answer

$$y^2 = mx + b$

Question 16

If a vertical line passes through $$(3, 2)$$, what is its equation?

Accepted Answer

$$x = 3$$

Question 17

A horizontal line passes through the point $$(0, 3). $$What is its equation?

Accepted Answer

$$y = 3$$

Question 18

If you use the linear model $$y = -4(x - 2008) + 55 to $$estimate sales in 2023, what type of prediction is this?

Accepted Answer

Extrapolation

Question 19

Which of the following is the correct process to find the $$x-$$intercept of the line $$Ax + By = C$$?

Accepted Answer

Let $$y = 0$$ and solve for $$x$$

Question 20

Which of the following best describes the equation $$y = mx + b$$?

Accepted Answer

Slope-intercept form

Equations of Lines and Linear Modeling in College Algebra

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