Graphing Functions

#33

Vocabulary

Linear equations-an equation whose solutions form a straight line on a coordinate plane Ex: y = 2 x + 1

Example 1

Use the given x-values to write solutions of the equation y = 4x + 2 as ordered pairs. x = 1, 2, 3, 4.

FYI

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.

Example 2

Determine whether the ordered pair is a solution to the given equation.

(3, 21); y = 7x

Example 3

Determine whether the ordered pair is a solution to the given equation.

(4, 20); y = 5x

Example 4

Determine whether the ordered pair is a solution to the given equation.

(6, 4); y = 2x - 7

FYI

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.

Example 5

Use the graph of the linear function to find the value of y for the given value of x.

x = 4

x

y

-4 -2 0 2 4

4

-2

-4

2

Example 6For 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

Example 7For 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

Example 8

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

Example 9

Graph the function described by the equation. y = 3x+ 2

83(2) + 22

53(1) + 21

23(0) + 20

y3x + 2x