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A4.c How Do I Graph Equations Of The Form y = mx + b ?
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpSolve 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
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
y = –2x + 6
y = x + 852
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
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
Learn to identify and graph linear equations.
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
Vocabulary
Linear equation
Insert Lesson Title Here
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
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.
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
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.
3
3
3
2
2
2
Course 3
A4.c How Do I Graph Equations Of The Form
y = mx + b ?
Graph the equation and tell whether it is linear.
y = 3x – 1
Example 1A: Graphing Equations
x 3x – 1 y (x, y)
–2
–1
0
1
2
–73(–2) – 13(–1) – 1
3(0) – 13(1) – 1
3(2) – 1
–4
–1
2
5
(–2, –7)
(–1, –4)(0, –1)
(1, 2)(2, 5)
Course 3
A4.c How Do I Graph Equations Of The Form y
= mx + b ?
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.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Insert Lesson Title Here
Be careful when graphing each ordered pair. Double check each point you plot.
Caution!
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Graph the equation and tell whether it is linear.
y = 2x + 1
Check it Out: Example 1A
x 2x + 1 y (x, y)
–4
–2
0
2
4
–72(–4) + 12(–2) + 1
2(0) + 12(2) + 1
2(4) + 1
–3
1
5
9
(–4, –7)
(–2, –3)(0, 1)
(2, 5)(4, 9)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 1A Continued
The equation y = 2x + 1is linear equation because it is the graph of a straight line and each time x increases by 1 unit, y increases by 2 units.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Graph the equation and tell whether it is linear.
y = x3
Example 1B: Graphing Equations
x x3 y (x, y)
–2
–1
0
1
2
–8(–2)3
(–1)3
(0)3
(1)3
(2)3
–1
0
1
8
(–2, –8)
(–1, –1)(0, 0)
(1, 1)(2, 8)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
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.
x –2 –1 0 1 2
y –8 –1 0 1 8
+7 +1 +1 +7Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Graphing the equation and tell whether it is linear.
y = x2
Check It Out: Example 1B
x x2 y (x, y)
–2
–1
0
1
2
4(–2)2
1
0
1
4
(–2, 4)
(–1, 1)(0, 0)
(1, 1)(2, 4)
(–1)2
(0)2
(1)2
(2)2
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 1B Continued
The equation y = x2 is not a linear equation because its graph is not a straight line. It is called nonlinear.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Example 1C: Graphing EquationsGraph the equation and tell whether it is linear.
y = – 3x4
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Example 1C Continued
The equation y = –
is a linear equation
because the points form
a straight line. Each
time the value of x
increases by 1, the
value of y decreases by
or y decreases by 3
each time x increases
by 4.
3x4
34
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 1C
Graph the equation and tell whether it is linear.
y = x
x y (x, y)
–8
–6
0
4
8
–8
–6
0
4
8
(–8, –8)
(–6, –6)(0, 0)
(4, 4)(8, 8)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 1C Continued
The equation y = x is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y increases by 1.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Graph the equation and tell whether it is linear.
y = 2
Example 1D: Graphing Equations
For any value of x, y = 2.
x 2 y (x, y)
–2
–1
0
1
2
222
2
2
2
2
2
2
2
(–2, 2)
(–1, 2)(0, 2)
(1, 2)(2, 2)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
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 (the value of y stays the same).
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 1D
For any value of x, y = 7.
Graph the equation and tell whether it is linear.
D. y = 7x 7 y (x, y)
–8
–4
0
4
8
777
7
7
7
7
7
7
7
(–8, 7)
(–4, 7)(0, 7)
(4, 7)(8, 7)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: 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.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
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.
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Example 2 Continued
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Example 2 Continued
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
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.
Example 2 Continued
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: 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?
Rider Time
Ryan 1 min
Greg 2 min
Colette 3 min
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Check It Out: Example 2 Continued
t D =1250t D (t, D)
1 1250(1) 1250 (1, 1250)
2 1250(2) 2500 (2, 2500)
3 1250(3) 3750 (3, 3750)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
The distances are: Ryan, 1250 ft; Greg, 2500 ft; and Collette, 3750 ft.
Check It Out: Example 2 Continued
x
y
This is a linear equation because when t increases by 1 unit, D increases by 1250 units.
1250
2500
1 2
3750
5000
3 4Time (min)
Dis
tan
ce (
ft)
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
Lesson QuizGraph each equation and tell whether it is linear.
1. y = 3x – 1
2. y = x
3. y = x2 – 3
yes
yes
Insert Lesson Title Here
no
14
Course 3
A4.c How Do I Graph Equations Of The Form y = mx + b ?
