Graphing Linear Equations

1
Graphing Linear Equations
11-1
Warm Up
Problem of the Day
Lesson Presentation
2
Warm Up Solve each equation for y. 1. 6y 12x
24 2. 2y 4x 20 3. 2y 5x 16 4. 3y 6x
18
y 2x 4
y 2x 10
y 2x 6
3
Problem of the Day The same photo book of
Niagara Falls costs 5.95 in the United States
and 8.25 in Canada. If the exchange rate is
1.49 in Canadian dollars for each U.S. dollar,
in which country is the book a better deal?
Canada
4
Learn to identify and graph linear equations.
5
Vocabulary
linear equation
6
A linear equation is an equation whose solutions
fall on a line on the coordinate plane. All
solutions of a particular linear equation fall on
the line, and all the points on the line are
solutions of the equation. To find a solution
that lies between two points (x1, y1) and (x2,
y2), choose an x-value between x1 and x2 and find
the corresponding y-value.
7
Reading Math
Read x1 as x sub one or x one.
8
If an equation is linear, a constant change in
the x-value corresponds to a constant change in
the y-value. The graph shows an example where
each time the x-value increases by 3, the y-value
increases by 2.
2
3
2
3
2
3
9
Additional Example 1A Graphing Equations
Graph the equation and tell whether it is
linear. A. y 3x 1
7
3(2) 1
(2, 7)
3(1) 1
4
(1, 4)
(0, 1)
3(0) 1
1
3(1) 1
2
(1, 2)
(2, 5)
3(2) 1
5
10
Additional Example 1A Continued
The equation y 3x 1 is a linear equation
because it is the graph of a straight line and
each time x increases by 1 unit, y increases by 3
units.
11
Additional Example 1B Graphing Equations
Graph the equation and tell whether it is
linear. B. y x3
8
(2)3
(2, 8)
(1)3
1
(1, 1)
(0, 0)
(0)3
0
(1)3
1
(1, 1)
(2, 8)
(2)3
8
12
Additional Example 1B Continued
The equation y x3 is not a linear equation
because its graph is not a straight line. Also
notice that as x increases by a constant of 1
unit, the change in y is not constant.
7
1
1
7
13
Additional Example 1C Graphing Equations
Graph the equation and tell whether it is
linear. C. y
14
Additional Example 1 Continued
15
Additional Example 1D Graphing Equations
Graph the equation and tell whether it is
linear. D. y 2
2
2
(2, 2)
2
2
(1, 2)
(0, 2)
2
2
2
2
(1, 2)
(2, 2)
2
2
For any value of x, y 2.
16
Additional Example 1D Continued
The equation y 2 is a linear
equation because the points form a straight line.
As the value of x increases, the value of y has a
constant change of 0.
17
Try This Example 1A
Graph the equation and tell whether it is
linear. A. y 2x 1
3
2(2) 1
(3, 3)
2(1) 1
1
(2, 1)
(1, 1)
2(0) 1
1
2(1) 1
3
(0, 3)
(2, 5)
2(2) 1
5
18
Try This Example 1A Continued
The equation y 2x 1is linear equation
because it is the graph of a straight line and
each time x increase by 1 unit, y increases by 2
units.
19
Try This Example 1B
Graphing the equation and tell whether it is
linear. B. y x2
4
(2)2
(2, 4)
1
(1, 1)
(1)2
(0, 0)
0
(0)2
(1)2
1
(1, 1)
(2, 4)
(2)2
4
20
Try This Example 1B Continued
The equation y x2 is not a linear equation
because its graph is not a straight line.
21
Try This Example 1C
Graph the equation and tell whether it is
linear. C. y x
8
(8, 8)
6
(6, 6)
(0, 0)
0
4
(4, 4)
(8, 8)
8
22
Try This Example 1C Continued
23
Try This Example 1D
Graph the equation and tell whether it is
linear. D. y 7
7
7
(8, 7)
7
7
(4, 7)
(0, 7)
7
7
7
7
(4, 7)
(8, 7)
7
7
For any value of x, y 7.
24
Try This Example 1D Continued
The equation y 7 is a linear
equation because the points form a straight line.
As the value of x increases, the value of y has a
constant change of 0.
25
Additional Example 2 Sports Application
A lift on a ski slope rises according to the
equation a 130t 6250, where a is the altitude
in feet and t is the number of minutes that a
skier has been on the lift. Five friends are on
the lift. What is the altitude of each person if
they have been on the ski lift for the times
listed in the table? Draw a graph that represents
the relationship between the time on the lift and
the altitude.
26
Additional Example 2 Continued
27
Additional Example 2 Continued
28
Additional Example 2 Continued
The altitudes are Anna, 6770 feet Tracy, 6640
feet Kwani, 6510 feet Tony, 6445 feet George,
6380 feet. This is a linear equation because
when t increases by 1 unit, a increases by 130
units. Note that a skier with 0 time on the lift
implies that the bottom of the lift is at an
altitude of 6250 feet.
29
Try This Example 2
In an amusement park ride, a car travels
according to the equation D 1250t where t is
time in minutes and D is the distance in feet the
car travels. Below is a chart of the time that
three people have been in the cars. Graph the
relationship between time and distance. How far
has each person traveled?
30
Try This Example 2 Continued
The distances are Ryan, 1250 ft Greg, 2500 ft
and Collette, 3750 ft.
31
Try This Example 2 Continued
y
5000
3750
Distance (ft)
2500
1250
x
1
2
3
4
Time (min)
This is a linear equation because when t
increases by 1 unit, D increases by 1250 units.
32
Lesson Quiz
Graph each equation and tell whether it is
linear. 1. y 3x 1 2. y x 3. y x2
3
yes
yes
no