Lesson 10: Linear Functions, Part 1
Linear functions are such a part of our everyday life that usually we don’t even
realize it. Many of the characteristics of linear functions are taken as common
sense. In this lesson, we take a closer look at those characteristics and investigate
how to make use of them. We also investigate the special case of a linear equation
that is not a linear function, the vertical line.
Mini-Lesson
Section 10.1: Linear Functions
Section 10.2: Graphing Linear Functions
Section 10.3: Interpreting the Slope of a Linear Function
Section 10.4: The Equation of a Linear Function
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Name: ________________________________
Date: _____________
Mini-Lesson 10 Section 10.1: Linear Functions
LINEAR FUNCTIONS
SLOPE =
Change in OUTPUT
Change in INPUT
Slope
Example 1: Determine the slope for each of the following:
a. (!2, 3) and ( 4, !1)
b. (!3, !1) and
( 4, 2)
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Lesson 10: Linear Functions, Part I
Mini-Lesson
c. (3, 2 ) and (!1, 2 )
d. ( 2, !3) and
(2,1)
You Try
1.
Determine the slope of the line between the given points.
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(!4, !1)
and ( 5, !6 )
Introductory Algebra
Lesson 10: Linear Functions, Part I
Mini-Lesson
Section 10.2: Graphing Linear Functions
USING THE SLOPE TO GRAPH A LINEAR FUNCTION
SLOPE =
Change in OUTPUT
Change in INPUT
Example 1: Draw an accurate graph for each of the following
1
2
a. (!2, !3) slope
b. ( 0, !1) slope !
2
3
c. ( 2,1) slope 3
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d. (1, !4) slope 0
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Lesson 10: Linear Functions, Part I
Mini-Lesson
e. (5, 2) undefined slope
You Try
2.
3
Sketch the graph of a linear function that passes through the point (!3, 4) with slope = ! .
2
Your line must extend accurately from
edge to edge of the graph shown
Give the coordinates of two additional
points
on the line.
_____________
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_____________
Introductory Algebra
Lesson 10: Linear Functions, Part I
Mini-Lesson
Section 10.3: Interpreting the Slope of a Linear Function
SLOPE =
Change in OUTPUT
Change in INPUT
Units of the slope:
Example 1: This graph shows the amount of water in a tub over a ten-minute time period.
a. Identify the vertical intercept and interpret its meaning.
b. Identify the horizontal intercept and interpret its meaning.
c. Determine the slope, and interpret its meaning.
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Introductory Algebra
Lesson 10: Linear Functions, Part I
Mini-Lesson
You Try
3. The graph below shows Sally’s distance from home over a 30 minute time period.
a. Identify the vertical intercept. Write it as an ordered pair and interpret its meaning.
b. Identify the horizontal intercept. Write it as an ordered pair and interpret its meaning.
c. Determine the slope, and interpret its meaning.
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Lesson 10: Linear Functions, Part I
Mini-Lesson
Section 10.4: The Equation of a Linear Function
Slope – Intercept Form
SLOPE-INTERCEPT FORM: y = mx + b
y = b + mx
f(x) = mx + b
Example 1: Fill in the table below.
Equation
Slope
I, D, H, V
Vertical Intercept
y = 3x + 5
y=8–x
y = 2x
y = −8
Example 2: Determine the horizontal intercepts of each of the following.
a. y = 3x + 5
b. y = 8 ! x
c. y = 2x
d. y = !8
Example 3: The equation of a vertical line.
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Lesson 10: Linear Functions, Part I
Mini-Lesson
Example 4: Draw an accurate graph of the function f (x) = 4 – 3x.
Slope: ___________
Vertical Intercept: ____________
Horizontal Intercept: ____________
Two additional points on the line:
____________
_____________
You Try
4. Fill in the table below. Write intercepts as ordered pairs.
I = Increasing, D = Decreasing, H = Horizontal (Constant), V = Vertical
Equation
Slope
I, D, H, V
Vertical Intercept
y = x − 11
G ( x ) = !2x
x=5
5. Draw and accurate graph of the function y =
3
x!5.
4
Slope: ___________
Vertical Intercept: _____________
Horizontal Intercept: _____________
Two additional points on the line:
____________
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Introductory Algebra