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

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

Question 1

Given the points $$A(-2,4)$$ and $$B(3,-6)$$, what is the slope of the line passing through these points?

Accepted Answer

$$m = -2$$

Question 2

Which of the following equations is the correct point-slope form for the line passing through $$(-2,4)$$ with slope $$-2$$?

Accepted Answer

$$y - 4 = -2(x + 2)$$

Question 3

Convert the equation $$y - 4 = -2(x + 2) to $$standard form $$Ax + By = C.$$

Accepted Answer

$$2x + y = 0$$

Question 4

If two nonvertical lines in the Cartesian plane are parallel, which of the following must be true?

Accepted Answer

Their slopes are equal.

Question 5

Which of the following pairs of lines are perpendicular?

Accepted Answer

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

Question 6

Given the equation $$3x - 6y = -12$$, what is the slope of the line?

Accepted Answer

$$m = \frac{1}{3}$$

Question 7

Which of the following statements is true about the lines $$y = -\frac{3}{2}x + 1$$ and $$3x + 2y = 6$$?

Accepted Answer

They are perpendicular.

Question 8

A city planner wants to design two roads that are perpendicular. If the first road has a slope of $$\frac{3}{4}$$, what must be the slope of the second road?

Accepted Answer

$$-\frac{4}{3}$$

Question 9

Which of the following is the correct $$y-$$intercept for the line defined by $$-3x + 5y = 20$$?

Accepted Answer

$$y-$$intercept is $$4$$

Question 10

Given the lines $$y = \frac{1}{2}x + 3$$ and $$2x - y = 4$$, determine their relationship.

Accepted Answer

They are neither parallel nor perpendicular.

Question 11

A biologist is tracking two migrating animals. The first animal moves along the path $$y = 2x + 5$$, and the second along $$y = -\frac{1}{2}x + 1. $$What is the relationship between their paths?

Accepted Answer

The paths are perpendicular.

Question 12

Which of the following is the correct standard form of the equation for a line with slope $$-3$$ and $$y-$$intercept $$2$$?

Accepted Answer

$$3x + y = 2$$

Question 13

If two lines have slopes $$m_1$$ and $$m_2$$, which of the following must be true for the lines to be perpendicular?

Accepted Answer

$$m_1$$ $$m_2 = -1$

Question 14

A vertical line and a horizontal line in the Cartesian plane are always:

Accepted Answer

Perpendicular

Question 15

Given the equation $$4x + 6y = 12$$, what is the slope of the line?

Accepted Answer

$$m = -\frac{2}{3}$$

Question 16

A road is constructed along the line $$x = 5. $$What is the slope of this road?

Accepted Answer

Undefined

Question 17

Which of the following best describes the relationship between the lines $$x = 1$$ and $$x = 2$$?

Accepted Answer

They are parallel.

Question 18

A chemist is graphing the reaction rate as a function of temperature. If the data fits the line $$y = 0.5x + 10$$, what is the reaction rate when the temperature is $$20$$ degrees?

Accepted Answer

$$y = 20$$

Question 19

Given the points $$A(1,2)$$ and $$B(5,10)$$, what is the equation of the line passing through them in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 20

A medical researcher finds that the number of cases of a disease increases linearly with time. If there were $$100$$ cases at year $$0$$ and $$250$$ cases at year $$3$$, what is the equation for the number of cases $$y as a $$function of time $$x (in $$years)?

Accepted Answer

$$y = 50x + 100$$

Slopes, Equations of Lines, and Relationships Between Lines in the Cartesian Plane

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