Warm Up Problem Identify the terms like terms
Warm Up Problem �Identify the terms, like terms, coefficients, and constants in the expression below. � 4 y + 5 + 3 y
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. Input, x 1 2 3 4 5 Output, y 9 18 27 36 45 Input, x 1 2 3 4 5 1(9) 2(9) 3(9) 4(9) 5(9) 9 18 27 36 45 Output, y The value of y is equal to 9 times the value of x. So, the equation that represents the function is y = 9 x.
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 = 2 x. x 0 1 2 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. 2 x 2(0) 2(1) 2(2) y 0 2 4 (x, y) (0, 0) (1, 2) (2, 4) 5 4 3 2 1 0 0 2 4
Got It? Graph each equation. 2) y = x + 1 3) y = 3 x + 2
Example 3 Adrian constructed the graph shown, which shows the height of his cactus after several years of growth. 48 46 44 42 Make a function table for the inputoutput values. The input values are 1, 2, and 3 and the output values are 42, 44, and 46. 40 0 1 Input (x) 1 2 3 4 Output (y) 42 44 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 2 x. The output value for 1 is 42. 2(1) = 2 so 42 is 40 more than that. So the equation is y = 2 x + 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. 40 35 30 25 20 0 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. 1 2 3 4 5
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