AnswersPARTA - EOP PGCPS GEOMETRY OC FALL2026 - 793413Slopes of Parallel and Perpendicular Lines

Slopes of Parallel and Perpendicular Lines — Unit test Answers

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What is the equation of the line in slope-intercept form that is perpendicular to the line y = x – 2 and passes through the point (–12, 10)?

Question illustration
A
y = x – 6
Option A
B
y = x + 6
Option B
C
y = x + 26
Option C
D
y = x + 10
Option D
2
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What is the equation of the line that is perpendicular to the line y = 6 and passes through the point (–4, –3)?

A
x = –4
B
x = –3
C
x =
Option C
D
x = 6
3

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

A
y = –3x
B
y = –
Option B
C
y =
Option C
D
y = 3x
4

A coordinate plane with a line passing through points at (0, negative 2) and (4, negative 1).

Question illustration
A
y = 4x – 2
B
y = –4x – 2
C
y = x – 2
Option C
D
y = – x – 2
Option D
5

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

A
–15
B
–9
C
3
D
9
6

On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0).

Question illustration
A
They are parallel because their slopes are equal.
B
They are parallel because their slopes are negative reciprocals.
C
They are not parallel because their slopes are not equal.
D
They are not parallel because their slopes are negative reciprocals.
7

A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)

Question illustration
A
The slope of g(x) is the opposite of the slope of f(x).
B
The slope of g(x) is less than the slope of f(x).
C
The slope of g(x) is greater than the slope of f(x).
D
The slope of g(x) is equal to the slope of f(x).
8

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

A
y = –3x
B
y = –
Option B
C
y =
Option C
D
y = 3x
9

A coordinate plane with a line passing through points at (0, negative 2) and (4, negative 1).

Question illustration
A
y = 4x – 2
B
y = –4x – 2
C
y = x – 2
Option C
D
y = – x – 2
Option D
10

A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = (x – 2). Which equations also represent this line? Select three options.

Question illustration
A
y = x – 2
Option A
B
y = x +
Option B
C
3y = –5x + 10
D
3x + 15y = 30
E
5x + 3y = 10
11

A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

A
The line represents a direct variation because = .
Option A
B
The line represents a direct variation because it is horizontal.
C
The line does not represent a direct variation because it does not go through the origin.
D
The line does not represent a direct variation because –4(3) ≠ 4(3).
12

Mrs. Jackson gives the table below to her students.

Question illustration
A
a = 22 because the rate of change is 1.
B
a = 20 because the rate of change is 3.
C
a = 22 because the rate of change is –1.
D
a = 20 because the rate of change is –3.
13

At a glance, Kendra believes that the function represented on the graph is linear.

Question illustration
A
She can check to see if the rate of vertical increase equals the rate of horizontal increase between each pair of points.
B
She can check to see if the sum of each y-value and x-value in every ordered pair is the same.
C
She can check to see if the quotient of each y-value and x-value in every ordered pair is the same.
D
She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.
14

Which table represents a linear function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

What is the slope of a line that is perpendicular to the line x = –3?

A
–3
B
0
C
Option
Option C
D
undefined
16

What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)?

A
Option
Option A
B
Option
Option B
C
3
D
6
17

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

A
–15
B
–9
C
3
D
9

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