5-2 Use Linear Equations in Slope-Intercept Form

Warm Up Find the slope of the line that goes through the points 1. (0, -2), (1, 3) 2. (3, 2), (5, -2) 3. Bill borrowed $75 dollars from his parents. He is paying back $5 per week. Write an equation that models this situation.

Writing Equations of Lines that Don’t Have a Clear Y-intercept 1.Find the slope using two points on the line. 2.Substitute slope for m in y = mx + b. 3.Choose any point on the line (x, y) and substitute it in to the equation. 4.The only variable left is b, solve for b. 5.Re-write the equation with the slope and y-intercept you found.

Example 1 Write an equation of a line that goes through (-1, 3) and has a slope of -4.

Extra Example 1 Write an equation that has a slope of 5 and goes through (4, -1).

Guided Practice #1 Write an equation of the line that passes through the point (6, 3) and has a slope of 2.

When you aren’t given slope… Find it! Write an equation of the line that passes through (-2, 5) and (2, -1)

Extra Example 2 Write an equation of a line that goes through (2, -1) and (4, -3).

Guided Practice #2 Write an equation of the line that passes through (1, -2) and (-5, 4).

Review How do you write an equation in y = mx + b when you don’t automatically know b?

Homework 5.2a 1, 4 – 22 evens, 55 – 58

5.2b Writing Linear Equations in Slope-Intercept Form Function Notation, Working with Real-Life Problems

Function Notation Write an equation that has values f(4) = 9 and f(-4) = -7.

Guided Practice #3 Write an equation for the function with values f(-2) = 10 and f(4) = -2.

One more? Write an equation for the linear function with values f(2) = 8 and f(-2) = -4.

Solve a multi-step problem EXAMPLE 4 Your gym membership costs $33 per month after an initial membership fee. You paid a total of $228 after 6 months. Write an equation that gives the total cost as a function of the length of your gym membership (in months). Find the total cost after 9 months. STEP 1 Identify the rate of change and starting value. GYM MEMBERSHIP SOLUTION

Solve a multi-step problem EXAMPLE 4 Rate of change, m: monthly cost, $33 per month STEP 2 Write a verbal model. Then write an equation. C= t b 33+ Starting value, b: initial membership fee

Solve a multi-step problem EXAMPLE 4 Find the starting value. Membership for 6 months costs $228, so you can substitute 6 for t and 228 for C in the equation C = 33t + b. 228 = 33(6) + b Substitute 6 for t and 228 for C. 30 = b Solve for b. STEP 3

Solve a multi-step problem EXAMPLE 4 C = 33t + 30 Substitute 30 for b. STEP 5 Evaluate the function when t = 9. C = 33(9) + 30 = 327 Substitute 9 for t. Simplify. STEP 4 Write an equation. Use the function from Step 2. Your total cost after 9 months is $327. ANSWER

Extra Example 4 A carnival charges $2.50 per ride after an entrance fee. You paid a total of $22.50 after 6 rides. Write an equation that give the total cost as a function of the number of rides. Find the total cost for 15 rides.

EXAMPLE 5 Solve a multi-step problem BMX RACING In Bicycle Moto Cross (BMX) racing, racers purchase a one year membership to a track. They also pay an entry fee for each race at that track. One racer paid a total of $125 after 5 races. A second racer paid a total of $170 after 8 races. How much does the track membership cost ? What is the entry fee per race ?

EXAMPLE 5 Solve a multi-step problem SOLUTION STEP 1 Identify the rate of change and starting value. Rate of change, m: entry fee per race Starting value, b: track membership cost STEP 2 Write a verbal model. Then write an equation. C = m r +b

EXAMPLE 5 Solve a multi-step problem STEP 3 Calculate the rate of change. This is the entry fee per race. Use the slope formula. Racer 1 is represented by (5, 125). Racer 2 is represented by (8, 170). 45 m = y 2 – y 1 x 2 – x 1 = 170 – – 5 = 3 =15 STEP 4 Find the track membership cost b. Use the data pair (5, 125) for racer 1 and the entry fee per race from Step 3.

EXAMPLE 5 Solve a multi-step problem Write the equation from Step 2. C = mr + b Substitute 15 for m, 5 for r, and 125 for C. 125 = 15(5) + b Solve for b. 50 = b ANSWER The track membership cost is $50. The entry fee per race is $15.

GUIDED PRACTICE for Examples 4 and 5 4. A gym charges $35 per month after an initial membership fee. A member has paid a total of $250 after 6 months. Write an equation that gives the total cost of a gym membership as a function of the length of membership (in months). Find the total cost of membership after 10 months. GYM MEMBERSHIP C = 35m + 40; $390 ANSWER

GUIDED PRACTICE for Examples 4 and 5 BMX RACING 5. A BMX race track charges a membership fee and an entry fee per race. One racer paid a total of $76 after 3 races. Another racer paid a total of $124 after 7 races. a. How much does the track membership cost ? ANSWER $40

GUIDED PRACTICE for Examples 4 and 5 BMX RACING 5. A BMX race track charges a membership fee and an entry fee per race. One racer paid a total of $76 after 3 races. Another racer paid a total of $124 after 7 races. b. What is the entry fee per race ? ANSWER $12

GUIDED PRACTICE for Examples 4 and 5 BMX RACING 5. A BMX race track charges a membership fee and an entry fee per race. One racer paid a total of $76 after 3 races. Another racer paid a total of $124 after 7 races. c. Write an equation that gives the total cost as a function of the number of races entered. ANSWER C = 12r + 40

Example For science class, you need to know the Celsius equivalent of a room temperature of 70 ۫ F. To estimate the Celsius equivalent, you use the facts that 32 ۫ F is equivalent to 0 ۫ C. and that 212 ۫ F is equivalent to 100 ۫ C. Estimate the Celsius equivalent of 70 ۫ F.

Homework 5.2b 23 – 28, 47, , Bonus: 46, 54