1. Algebra 1 EOC Summer School Lesson 9: Interpret the effects of changing slope and y-intercept

2. Introduction to the effects of changing m and b In the last lesson, we changed the value of m an b in an equation and looked at the effects on a graph In this lesson, we will change the value of m and b in a word problem and see how those changes effect the situation

3. What is m? m represents the slope of a line In a word problem slope can be: – The speed of a vehicle – The % commission an employee receives – A monthly payment – Any repeating cost (monthly, weekly, hourly…)

4. What is b? b represents the y-intercept of a line In a word problem the y-intercept can be: – A base fee – A service charge – A down payment – The starting point – Any one-time cost

5. Effects of changing m Brad has 2 job offers. Company 1 will calculate his paycheck using the equation p = 0.15t + 550. Company 2 will calculate his paycheck using the equation p = 0.12t + 550. p represents his total paycheck and t represents his total sales. What changed? 0.15 changed to 0.12 What do those numbers represent? Slope Or a % of Brad’s total sales

6. Effects of changing b A handyman charges an hourly rate plus a service charge to make repairs for customers. He currently uses the equation t = 25h + 15 to calculate the charge for each customer. t represents the total charge and h represents the number of hours he works on a job. How will the equation change if he raises his service charge to $30? What will the new equation be? t = 25h + 30 Which value in the equation will change? Y-intercept The service charge (15)

7. Effects of Changing m and b A car rental company calculates the cost of renting a mid-size car using the formula y = 0.15x + 20 where y is the total cost and x is the number of miles driven. If the company increases the cost per mile by $0.05 but decreases the base fee to $10, what equation can be used to calculate the new rental cost? Change to m +0.05 Old equationy = 0.15x + 20 Change to b 10 New equationy = 0.2x + 10

8. Making predictions A car rental company calculates the cost of renting a mid-size car using the formula y = 0.15x + 20 where y is the total cost and x is the number of miles driven. If the company increases the cost per mile by $0.05 but decreases the base fee to $10, what equation can be used to calculate the new rental cost? How would the cost change if a customer rented a car and drove it 150 miles? New equation y = 0.2x + 10 Old Equation y = 0.15x + 20 y = 0.15(150) + 20y = 0.2(150) + 10 y = $42.50y = $40