Warm Up Problem Identify the terms, like terms, coefficients, and constants in the expression below. 4y + 5 + 3y

Functions and Equations Lesson 8-3

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

Vocabulary linear function – a function whose graph is a line

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)

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

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)

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

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

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.

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.