1. Warm up F(x) = 2x + 4G(x) = 3x – 1 F(13) = G(10) = F(x) = 20 find x G(x) = 8 find x

2. Linear Function INTRO TO LINEAR FUNCTION

3. 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

4. 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 ) = 7x + 5

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 1: Identify the constant rate of change (m) f ( x ) = 300x + b Constant Rate of Change is $300 Step 2: Identify the initial value (b) Initial Value is $40,000 f ( x ) = 300x + 4000

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

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

8. Practice