Download Lesson 15 Representing Linear Functions

Lesson 15
Representing Linear Functions
TAKS Grade 9 Objective 3
(A.5)(C)
Linear functions can be represented by equations, tables, graphs, and
descriptions.
New Vocabulary
• slope-intercept
form
• slope
• y-intercept
Translating from Algebra to Charts and Graphs
To translate an equation into a table or a graph, generate a set of points
that satisfy the equation.
A newspaper advertisement costs $4, plus $5 for each line of text. Write an equation for
the cost of an advertisement. Then evaluate the equation to find the cost of a 1-line ad,
a 2-line ad, a 3-line ad, and a 4-line ad. Model the equation with a table, and then graph
your results.
Step 1 Write an equation. Choose variables and relate them according to the problem
situation.
Let y represent the cost of an advertisement, and x represent the number of
lines of text in the ad.
The cost is equal to $4, plus $5 times the number of lines.
y 4 5x
Step 2 Make a table of values that shows
x
4 5x
y (x, y)
the cost y for the given numbers
1 4 5(1) 4 5
9 (1, 9)
of lines, x.
2 4 5(2) 4 10 14 (2, 14)
3
4 5(3) 4 15
19 (3, 19)
4
4 5(4) 4 20
24 (4, 24)
Step 3 Graph your results. Use the ordered pairs
in the table to sketch the graph. The points
should not be connected, because you cannot
buy fractions of a line.
y
Cost of Advertisement
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
EXAMPLE 1
20
15
10
5
O
2
4
6
8
x
Number of Lines of Text
Quick Check 1
1a. Model 8 4y 2x using a table of values and a graph.
1b. Carol painted black and white tiles for the floor in her kitchen. The number of white tiles was
32 plus 45 the number of black tiles. Write an equation for the number of white tiles in terms
of the number of black ones. Model the equation with a table and graph your results.
TAKS Review and Preparation Workbook
LESSON 15
■
Representing Linear Functions
43
TAKS Objective 3 (A.5)(C)
LESSON 15
Translating into Algebra
The slope-intercept form of a linear function relates y to x using the slope
and the y-intercept. The slope of a line is the ratio of the vertical change to
the horizontal change. To find the slope, divide the vertical change between
any two points (x1, y1) and (x2, y2) by the horizontal change between them:
y 2 y
slope x22 2 x11. The y-intercept is the y-coordinate of the point where a line
crosses the y-axis.
A line with positive
slope rises as it goes
to the right. A line with
negative slope falls as
it goes to the right.
To determine the equation of a line, find the slope and the y-intercept. Then
write the equation in slope-intercept form, y mx b, where m represents
the slope, and b represents the y-intercept.
EXAMPLE 2
A group of students made this graph for their class. Write an equation that could
represent this function.
Step 1 Find the slope and use it to replace the
y
4
m in the equation.
Two points on the graph are (4, 1) and
2
(4, 5). Use the definition of slope:
–4
y 2y
m x22 2 x11
4x
–2 O
–2
21
25
24 2 4
–4
34
Step 2 Find the y-intercept and use that number to replace b. The graph crosses the y-axis
at the point (0, 2). Thus, the y-intercept is 2. The equation is: y 34x 2.
Quick Check 2
2a. Find the equation of the function shown
in the following graph.
4
2b. Find the equation for the line passing
through the ordered pairs shown.
y
y (3, 9)
8
2
6
–4
–2 O
2
4x
4
–2
–4
(–1, 1)
–4
44
LESSON 15
■
Representing Linear Functions
–2
2
O
2
4
x
TAKS Review and Preparation Workbook
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
26
28
Name__________________________Class____________Date________
1 Which function includes the data set
{(3, 6), (4, 8), (8, 16)}?
4 Which points are included in the function
y x 8?
A yx3
F (0, 8), (1, 9), (1, 7)
B y x2
G (2, 6), (3, 11), (1, 7)
C yx6
J (2, 10), (4, 12), (5, 13)
H (3, 5), (4, 4), (9, 1)
D y 2x
5 Which graph represents the function
y 15x 3?
2 What is the equation of the line shown?
4
4
y
2
A
2
–4
–2 O
y
2
–4
–2 O
2
4x
2
4x
2
4x
2
4x
–2
4x
–4
–2
–4
4
Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.
F y 12x 2
G y 21x 2
y
2
B
–4
–2 O
–2
H y 2x 2
–4
J y 2x 2
4
3 Rebecca and Carlos sold posters for a school
fundraiser. Rebecca sold four more than half
the number of posters that Carlos sold.
Which equation could represent the number
of posters Rebecca sold in terms of the
number Carlos sold?
2
C
–4
–2 O
–2
–4
A r 12c 4
4
B r 2c 8
C r 2c 8
y
y
2
D
–4
–2 O
–2
D r 21c 4
–4
TAKS Review and Preparation Workbook
LESSON 15
■
Representing Linear Functions
45