Answers2026-2027 Florida Advanced Course and Test FACT College Algebra - Teacher Directed ResourcesIntroduction to Linear Functions

Introduction to Linear Functions — Unit test Answers

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To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

A
negative StartFraction 5 Over 2 EndFraction
Option A
B
negative StartFraction 2 Over 5 EndFraction
Option B
C
StartFraction 2 Over 5 EndFraction
Option C
D
StartFraction 5 Over 2 EndFraction
Option D
2
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The table represents a linear function.

Question illustration
A
–10
B
–5
C
5
D
10
3

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.

Question illustration
A
Tracie’s bus travels towards her home at an average speed of mile per minute.
Option A
B
Tracie’s bus travels towards her home at an average speed of 2 miles per minute.
C
Tracie’s bus travels away from her home at an average speed of mile per minute.
Option C
D
Tracie’s bus travels away from her home at an average speed of 2 miles per minute.
4

The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?

A
The depth of snow was 0.8 inches when the storm began, and 2.5 inches after the first hour of the storm.
B
The depth of snow was 1.7 inches when the storm began, and 0.8 inches of snow fell each hour.
C
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
D
The depth of snow was 3.3 inches when the storm began, and 2.5 inches of snow fell in 1 hour.
5

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
6

The table represents a linear function.

Question illustration
A
–8
B
–4
C
2
D
5
7

Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?

A
y – 12 = –5(x + 2)
B
y – 12 = 2(x + 2)
C
y + 12 = 2(x – 2)
D
y + 12 = –5(x – 2)
8

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
9

Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?

Question illustration
A
f(x) = x + 4
Option A
B
f(x) = x + 6
Option B
C
f(x) = x – 10
Option C
D
f(x) = x – 12
Option D
10

The table represents a linear equation.

Question illustration
A
y – 6 = (x – 2)
Option A
B
y – 6 = (x – 2)
Option B
C
y + 6 = (x + 2)
Option C
D
y + 6 = (x + 2)
Option D
11

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
12

Raphael graphed the functions g(x)=x+2 and f(x)=x−1. How many units below the y-intercept of g(x) is the y-intercept of f(x)?

Question illustration
A
−3 units
B
−1 units
C
2 units
D
3 units
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

Timmy writes the equation f(x) = x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)?

Question illustration
A
The line of g(x) is steeper and has a higher y-intercept.
B
The line of g(x) is less steep and has a lower y-intercept.
C
The line of g(x) is steeper and has a lower y-intercept.
D
The line of g(x) is less steep and has a higher y-intercept.
15

Which table represents a linear function?

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

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