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

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

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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