Q: Using your linear model, predict the price of a Toyota Corolla that is 4 years old.

$$y = -1178.33 \times 4 + 18168.33 = 13455.01$$

Question 1

Given the data on the ages and advertised prices of used Toyota Corollas, what is the slope of the line passing through the first and last data points? Express your answer as a fraction.

Accepted Answer

$$m = \frac{2850 - 16990}{13 - 1}$$

Question 2

Using the slope found in the previous question, what is the decimal value of the slope rounded to the nearest hundredth?

Accepted Answer

$$m \approx -1178.33$$

Question 3

What is the point-slope form of the equation for the line passing through the points $$(1, 16990)$$ and $$(13, 2850)$$?

Accepted Answer

$$y = -1178.33(x - 1) + 16990$$

Question 4

Convert the equation from point-slope form to slope-intercept form for the line through $$(1, 16990)$$ with slope $$-1178.33. $$What is the $$y-$$intercept?

Accepted Answer

$$y = -1178.33x + 18168.33$$

Question 5

Using your linear model, predict the price of a Toyota Corolla that is 4 years old.

Accepted Answer

$$y = -1178.33 	imes 4 + 18168.33 = 13455.01$$

Question 6

Which of the following is the correct slope-intercept form for a line with slope $$m = \frac{2}{3}$$ and $$y-$$intercept $$b = -5$$?

Accepted Answer

$$y = \frac{2}{3}x - 5$$

Question 7

Find the equation of the line in point-slope form that passes through $$(2, 3)$$ with slope $$m = \frac{1}{2}.$$

Accepted Answer

$$y = \frac{1}{2}(x - 2) + 3$$

Question 8

Which of the following equations represents a horizontal line?

Accepted Answer

$$y = 4$$

Question 9

Given the line $$y = -\frac{3}{8}x - 2$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$m = \frac{8}{3}$$

Question 10

Find the equation of the line parallel to $$y = \frac{1}{4}x - 4$$ that passes through the point $$(4, 5).$$

Accepted Answer

$$y = \frac{1}{4}x + 4$$

Question 11

Which of the following is the standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 12

If two lines are perpendicular and one has a slope of $$m = 2$$, what is the slope of the other?

Accepted Answer

$$m = -\frac{1}{2}$$

Question 13

Which of the following best describes the relationship between the age of a car and its price, based on the data provided?

Accepted Answer

The relationship is approximately linear with a negative slope.

Question 14

Given the equation $$3x + 5y = 15$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 3)$$

Question 15

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 7$$

Question 16

If a line passes through $$(2, 3)$$ and $$(−2, 1)$$, what is its slope?

Accepted Answer

$$m = \frac{3 - 1}{2 - (−2)} = \frac{2}{4} = \frac{1}{2}$$

Question 17

Which of the following best describes the slopes of parallel lines?

Accepted Answer

They are equal.

Question 18

A company models its revenue with the equation $$y = 500x + 2000$$, where $$x is $$the number of units sold. What does the $$y-$$intercept represent?

Accepted Answer

The initial revenue when no units are sold.

Question 19

Which of the following is the correct point-slope form for a line with slope $$-3$$ passing through $$(2, 5)$$?

Accepted Answer

$$y = -3(x - 2) + 5$$

College Algebra Study Guide: Equations of Lines and Linear Functions

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