Upload
cody-powell
View
212
Download
0
Embed Size (px)
Citation preview
10-2 Graphing Functions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
10-2 Graphing Functions
Warm UpWrite an equation for each function. Use your own variables.
1. The length of a wall is 4 ft more than three times the height.
2. The number of trading cards is 3 less than the number of buttons.
l = 3h + 4
c = b – 3
10-2 Graphing Functions
Problem of the Day
Steve saved $1.50 each week. How many weeks did it take him to save enough to buy a $45 skateboard?30
10-2 Graphing Functions
MA.6.A.3.6 Construct and analyze tables, graphs, and equations to describe linear functions…using…algebraic notation.
Also MA.6.A.3.2
Sunshine State Standards
10-2 Graphing Functions
Vocabulary
linear equation
10-2 Graphing Functions Additional Example 1: Finding Solutions of
Equations with Two Variables
Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.Make a function table by using the given values for x to find values for y.
184(4) + 24
144(3) + 23
104(2) + 22
64(1) + 21
y4x + 2x Write these solutions as ordered pairs.
(x, y)
(1, 6)
(2, 10)(3, 14)(4, 18)
10-2 Graphing Functions
Check It Out: Example 1
Use the given x-values to write solutions of the equation y = 5x + 3 as ordered pairs. x = 2, 3, 4.
235(4) + 34
185(3) + 33
135(2) + 32
(x, y)5x + 3x
(2, 13)
(3, 18)
(4, 23)
y
10-2 Graphing Functions
Check if an ordered pair is a solution of an equation by putting the x and y values into the equation to see if they make it a true statement.
10-2 Graphing Functions
Additional Example 2: Checking Solutions of Equations with Two Variables
Determine whether the ordered pair is a solution to the given equation.
(3, 21); y = 7x
y = 7x Write the equation.
21 = 7(3)?
21 = 21?
Substitute 3 for x and 21 for y.
So (3, 21) is a solution to y = 7x.
10-2 Graphing Functions
Check It Out: Example 2A
Determine whether the ordered pair is a solution to the given equation.
(4, 20); y = 5x
y = 5x
20 = 5(4)?
20 = 20
(4, 20) is a solution to y = 5x.
10-2 Graphing Functions
Check It Out: Example 2B
Determine whether the ordered pair is a solution to the given equation.
(2, 3); y = x + 1
y = x + 1
3 = 2 + 1?
3 = 3
(2, 3) is a solution to y = x + 1.
10-2 Graphing Functions
Check It Out: Example 2C
Determine whether the ordered pair is a solution to the given equation.
(6, 4); y = 2x - 7
y = 2 x – 7
4 = 2(6) - 7?
4 = 5
(6, 4) is not a solution to y = 2x - 7.
10-2 Graphing Functions
Check It Out: Example 2D
Determine whether the ordered pair is a solution to the given equation.
(5, 1); y = 3x - 12
y = 3x - 12
1 = 3(5) - 12 ?
1 = 3
(5, 1) is a solution to y = 3x - 12.
10-2 Graphing Functions
You can also graph the solutions of an equation on a coordinate plane. When you graph the ordered pairs of some functions, they form a straight line. The equations that express these functions are called linear equations.
10-2 Graphing Functions
Additional Example 3: Reading Solutions on Graphs
Use the graph of the linear function to find the value of y for the given value of x.
x = 4
When x = 4, y = 2.
Start at the origin and move 4 units right.
Move up until you reach the graph. Move left to find the y-value on the y-axis.
The ordered pair is (4, 2).
x
y
-4 -2 0 2 4
4
-2
-4
2
10-2 Graphing Functions
Check It Out: Example 3AFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 2
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 6
10-2 Graphing Functions
Check It Out: Example 3BFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 0
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 9
10-2 Graphing Functions
Check It Out: Example 3CFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 4
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 3
10-2 Graphing Functions
Check It Out: Example 3DFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 1
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 6
10-2 Graphing Functions
Check It Out: Example 3EFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 4
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 7
10-2 Graphing Functions
Check It Out: Example 3FFor each graph of a linear function, find the values of y for the values of x given below the graph.x = 7
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
y = 8
10-2 Graphing Functions
Additional Example 4: Graphing Linear Functions
Graph the function described by the equation. y = 3x+ 2
83(2) + 22
53(1) + 21
23(0) + 20
y3x + 2x
(0, 2)
(1, 5)
(2, 8)
10-2 Graphing Functions
Additional Example 4 Continued
y
2
x 1 2 3 4 5 6 7 8 9
9
87
65
0
1
3
4
10-2 Graphing Functions
Check it out : Example 4A
Graph the function described by the equation. y = x + 3
5(2) + 32
4(1) + 31
3(0) + 30
yx + 3x
(0, 3)
(1, 4)
(2, 5)
10-2 Graphing Functions
Check it out : Example 4A Continued
y
2
x 1 2 3 4 5 6 7 8 9
9
87
65
0
1
3
4
10-2 Graphing Functions
Check it out : Example 4B
Graph the function described by the equation. y = 2x + 5
92(2) + 52
72(1) + 51
52(0) + 50
y2x + 5x
(0, 5)
(1, 7)
(2, 9)
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
10-2 Graphing Functions
Check it out : Example 4C
Graph the function described by the equation. y = 3x + 3
93(2) + 32
63(1) + 31
33(0) + 30
y3x + 3x
(0, 3)
(1, 6)
(2, 9)
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
10-2 Graphing Functions
Check it out : Example 4D
Graph the function described by the equation. y = 8 - x
28 - 66
18 - 77
08 - 88
y8 - xx
(8, 0)
(7, 1)
(6, 2)
y
2
x 1 2 3 4 5 6 7 8 9 10
9
87
65
0
1
3
4
10
10-2 Graphing Functions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
10-2 Graphing Functions
Lesson Quiz
1. Use the given x-values to write solutions as ordered pairs to the equation y = 10x + 5 for x = 0, 1, 2, and 3.
2. Determine whether (4, 2) is a solution to the
equation y = 5x – 6.
No, 2 ≠ 5(4) – 6
(0, 5), (1, 15), (2, 25), (3, 35)
10-2 Graphing Functions
y
2
x 1 2 3 4 5 6 7 8 9
9
87
65
0
1
3
4
3. Graph the function described by the equation y = 5 – x.
Lesson Quiz Cont.
10-2 Graphing Functions
1. Use the given x-values to identify solutions as ordered pairs to the equation y = 7x + 4 for x = 1, 3, 5, and 7.
Lesson Quiz for Student Response Systems
10-2 Graphing Functions
2. Identify the graph of the function described by the equation y = x – 5.
A. B.
Lesson Quiz for Student Response Systems