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