1. Warm Up Problem
Identify the terms, like terms, coefficients, and constants in the expression below.
4y y

2. Functions and Equations
Lesson 8-3

3. Objectives I can write an equation to represent a function.
I can graph data from a function on a line graph.

4. Vocabulary
linear function – a function whose graph is a line

5. Example 1
Write an equation to represent the function shown in the table.
The value of y is equal to 9 times the value of x. So, the equation that represents the function is y = 9x.
Input, x 1 2 3 4 5
Output, y 9 18 27 36 45
Input, x 1 2 3 4 5
Output, y 9 18 27 36 45
1(9)
2(9)
3(9)
4(9)
5(9)

6. Got It?
1) Write an equation to represent the function shown in the table.
Input, x 1 2 3 4 5
Output, y 16 32 48 64 80

7. Example 2 Graph y = 2x. Step 1: Make a table of ordered pairs.
Select “nice” numbers for x. Substitute
these values for x to find y.
Step 2: Graph each ordered pair.
Draw a line through each point. x 2x y
(x, y)
2(0)
(0, 0) 1
2(1) 2
(1, 2)
2(2) 4
(2, 4)

8. Got It?
Graph each equation.
2) y = x + 1
3) y = 3x + 2

9. Example 3
Adrian constructed the graph shown, which shows the height of his cactus after several years of growth. Make a function table for the input-output values. The input values are 1, 2, and 3 and the output values are 42, 44, and 46.
Input (x)
Output (y) 1 42 2 44 3 46

10. Example 4
Write an equation from the graph that could be used to find the height y of the cactus after x years (refer to Example 3).
Since the values increase by 2, the equation includes 2x.
The output value for 1 is 42. 2(1) = 2 so 42 is 40 more than that.
So the equation is y = 2x + 40.

11. Got It?
4) The graph shows the total amount y that you spend if you buy one book and x magazines. Make a function table for the input-output values.
5) Write an equation from the graph that could be used to find the total amount y if you buy one book and x magazines.