# Linear Function INTRO TO LINEAR FUNCTION Linear Function

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Linear Function INTRO TO LINEAR FUNCTION

Linear Function A function that can be defined by f (x) = mx + b Such that m is the constant rate of change and b is the initial value

Creating Linear Function from context Step 1: Identify the constant rate of change (m) Step 2: Identify the initial value (b) Step 3: Plug into f (x) = mx + b Given that the constant rate of change is 7 and the initial value is 5, how would you model this as a linear function? f (x) = 7 x + 5

Example 1 A machine salesperson earns a base salary of \$40, 000 plus a commission of \$300 for every machine he sells. Write an equation that shows the total amount of income the salesperson earns, if he sells x machines in a year. Step initial value (b) Step 2: 1: Identifythethe constant rate of change (m) Constant Rate Change is \$300 Initial Value is of \$40, 000 f (x)= =300 x+ +400 b f (x)

Example 2 A The linear model that shows the total income for the salesperson in example 1 is f(x) = 300 x + 40, 000. (a) What would be the salespersonâ€™s income if he sold 150 machines? Since he sold 150 machines, we can find his total income by finding f(150) = 300(150) + 40, 000 \$85, 000

Example 2 B The linear model that shows the total income for the salesperson in example 1 is f(x) = 300 x + 40, 000. (b) How 60, 000 = 300 x many machines would the salesperson need to sell to earn 200 = x a \$100, 000 income? Answer: To the earnsalesperson a \$100, 000 income Since we know want to herthe \$100, 000, to to sellsale 200 Wesalesperson can find howwould many need he need by setting F(x) = \$100, 000 machines. 100, 000 = 300 x + 40, 000

Practice