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Linear Functions & Graphs — Concept Test
Definition · Graph & Translation · Slope
Page 1 of 2
Name
Date
Score
Questions
14
|
Format
Short Answer
|
✦ Write each concept as a complete sentence.
A
Definition of a Linear Function
1.
Write the
definition
of a linear function.
2.
In \( y = ax + b \), explain why the function is
not linear when \( a = 0 \)
.
3.
In \( y = ax + b \), what type of function results
when \( b = 0 \)
?
B
Graph & Vertical Translation
4.
What equation results when the graph of \( y = ax \) is
translated
vertically by \( b \) units?
5.
Describe the direction of the vertical translation when \( b > 0 \) and when \( b < 0 \), respectively.
C
Slope
6.
Define
slope
and write its formula.
(slope) \( = \)
7.
Describe whether the function is increasing or decreasing when \( a > 0 \) and when \( a < 0 \), respectively.
8.
Describe how the graph changes as the absolute value of the slope \( |a| \) increases.
Readers Math Academy
Linear Functions & Graphs — Concept Test
Intercepts · Finding the Equation · Relationship of Two Lines · Applications
Page 2 of 2
Name
Date
Score
Questions
14
|
Format
Short Answer
|
✦ Write each concept as a complete sentence.
D
Intercepts
9.
Define the
\( y \)-intercept
and the
\( x \)-intercept
of \( y = ax + b \).
Use the diagram below to support your answer.
x
y
O
p
x-int (p, 0)
q
y-int (0, q)
y-intercept:
x-intercept:
E
Finding the Equation of a Linear Function
10.
Describe how to find the equation of a line given its slope \( a \) and one point \( (x_1,\, y_1) \).
11.
Describe the steps for finding the equation of a line through two distinct points \( (x_1,\, y_1) \) and \( (x_2,\, y_2) \).
F
Relationship of Two Lines
12.
State the condition for \( y = ax + b \) and \( y = cx + d \) to be
parallel
.\n
Express your answer in terms of \( a,\, b,\, c,\, d \).
13.
State the condition for \( y = ax + b \) and \( y = cx + d \) to be
coincident
(identical).
G
Real-World Applications
14.
When a real-world situation is modelled by \( y = ax + b \), explain what the slope \( a \) and the \( y \)-intercept \( b \) each represent.