Q: Which of the following pairs of lines are perpendicular?

$$y = 2x + 1$$ \,\text{and}\, y = -\frac{1}{2}x + 3$

Q: A company tracks the cost of a product over several years and finds the best-fit regression line is $$y = 1.5x + 10$$, where $$x is $$years since 2010 and $$y is $$cost in dollars. What is the predicted cost in 2020?

$$y = 1.5 \times 10 + 10 = 25$$

Q: A real-world scenario: The cost of a 30-second commercial increases by $$0.3$$ million per year, starting at $$2.8$$ million in 2010. What is the predicted cost in 2018?

$$y = 0.3 \times 8 + 2.8 = 5.2$$

Question 1

A line passes through the point (5, -2) and has a slope of $$\frac{3}{4}. $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = \frac{3}{4}x - \frac{19}{4}$$

Question 2

Which of the following pairs of lines are perpendicular?

Accepted Answer

$$y = 2x + 1$$ \,	ext{and}\, y = -\frac{1}{2}x + 3$

Question 3

Given the line $$y = -\frac{2}{3}x + 4$$, which of the following is the equation of a line parallel to it and passing through the point (6, 1)?

Accepted Answer

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

Question 4

A company tracks the cost of a product over several years and finds the best-fit regression line is $$y = 1.5x + 10$$, where $$x is $$years since 2010 and $$y is $$cost in dollars. What is the predicted cost in 2020?

Accepted Answer

$$y = 1.5 	imes 10 + 10 = 25$$

Question 5

If the correlation coefficient $$r$$ for a set of data is $$-0.95$$, which statement best describes the relationship between $$x$$ and $$y$$?

Accepted Answer

There is a strong negative linear relationship.

Question 6

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

Accepted Answer

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

Question 7

Given the equations $$y = 4x - 7$$ and $$y = -\frac{1}{4}x + 2$$, are the lines parallel, perpendicular, or neither?

Accepted Answer

Perpendicular

Question 8

A vertical line $$x = 3$$ and a horizontal line $$y = -2$$ are:

Accepted Answer

Perpendicular

Question 9

A line has equation $$y = 5x + 2. $$What is the slope of a line perpendicular to it?

Accepted Answer

$$-\frac{1}{5}$$

Question 10

You are given two points: $$(1, 2)$$ and $$(4, 8). $$What is the equation of the line passing through these points in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 11

A set of data has a regression line $$y = -0.8x + 5$$ and $$r = -0.2. $$What does this indicate about the data?

Accepted Answer

There is a weak negative linear relationship.

Question 12

Which of the following is NOT a property of parallel lines?

Accepted Answer

They have different slopes.

Question 13

A real-world scenario: The cost of a 30-second commercial increases by $$0.3$$ million per year, starting at $$2.8$$ million in 2010. What is the predicted cost in 2018?

Accepted Answer

$$y = 0.3 	imes 8 + 2.8 = 5.2$$

Question 14

Which equation represents a line perpendicular to $$y = \frac{1}{2}x - 3$$ and passing through $$(0, 4)$$?

Accepted Answer

$$y = -2x + 4$$

Question 15

If a regression line for a dataset is $$y = 0.25x + 10$$ and $$r = 0.99$$, what does this tell you about the data?

Accepted Answer

There is a strong positive linear relationship.

Question 16

Which of the following is the correct definition of the point-slope form of a line?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 17

A mathematical model is considered valid if:

Accepted Answer

Its predictions match experimental results.

Question 18

Which of the following best describes curve fitting?

Accepted Answer

Finding a function that fits observations, theory, and common sense.

Question 19

Given the line $$y = -3x + 7$$, what is the equation of a line parallel to it passing through $$(2, 1)$$?

Accepted Answer

$$y = -3x + 7$$

Equations of Lines and Linear Modeling in Precalculus

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