Warm Up Lesson Presentation Lesson Quiz Write Linear Equations in Slope-Intercept Form Warm Up Lesson Presentation Lesson Quiz

Warm-Up Find the slope of the line that passes through the points. 1. (2, –1), (4, 0) 1 2 ANSWER 2. (–1, –3), (1, 5) ANSWER 4

Warm-Up 3. A landscape architect charges $75 for a consulting fee and $30 per hour. Write an equation that shows the cost C as a function of time t (in hours). ANSWER C = 30t + 75

Example 1 Write an equation of the line with a slope of –2 and a y-intercept of 5. y = mx + b Write slope-intercept form. y = –2x + 5 Substitute –2 for m and 5 for b.

Guided Practice Write an equation of the line with the given slope and y-intercept. 1. Slope is 8; y-intercept is –7. y = 8x – 7 ANSWER 2. Slope is ; y intercept is –3. 3 4 y = 3 4 x – 3 ANSWER

Which equation represents the line shown? Example 2 Which equation represents the line shown? A y = – x + 3 2 5 B C y = – x + 1 D y = 3x + = – The slope of the line is rise run –2 5 2 . The line crosses the y-axis at (0, 3). So, the y-intercept is 3. y = mx + b Write slope-intercept form. 2 y = – x + 3 5 2 Substitute – for m and 3 for b. 5

Example 2 ANSWER The correct answer is A. B D C A

Write an equation of the line shown. Example 3 Write an equation of the line shown. SOLUTION STEP 1 Calculate the slope. x2 – x1 3 3 – 0 y2 – y1 = m –1 – (–5) 4 STEP 2 Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5. y = mx + b Write slope-intercept form. y = x – 5 4 3 Substitute for m and 5 for b. 4 3

Guided Practice 3. Write an equation of the line shown. 2 1 x + 1 y = ANSWER –

Example 4 Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17. SOLUTION STEP 1 Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17). STEP 2 Calculate the slope of the line that passes through (0, 5) and (4, 17). x2 – x1 4 – 0 y2 – y1 = m 17 – 5 4 12 3

The function is f(x) = 3x + 5. Example 4 STEP 3 y = mx + b Write slope-intercept form. y = 3x + 5 Substitute 3 for m and 5 for b. ANSWER The function is f(x) = 3x + 5.

Guided Practice Write an equation for the linear function f with the given values. f(0) = –2, f(8) = 4 4. y = x – 2 3 4 ANSWER 5. f(–3) = 6, f(0) = 5 y = x + 5 1 3 ANSWER –

Example 5 Recording Studio A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour. Write an equation that gives the total cost of an album as a function of studio time (in hours). a. Find the total cost of recording an album that takes 10 hours of studio time. b.

Example 5 SOLUTION The cost changes at a constant rate, so you can write an equation in slope-intercept form to model the total cost. a. STEP 1 Identify the rate of change and the starting value. Rate of change, m: cost per hour Starting value, b: initial fee

Example 5 STEP 2 Write a verbal model. Then write the equation. C = t 35 + 50 Use unit analysis to check the equation. CHECK hour dollars = hours + dollars dollars The total cost C is given by the function C = 35t + 50 where t is the studio time (in hours). ANSWER

b. Evaluate the function for t = 10. Example 5 b. Evaluate the function for t = 10. C = 35(10) + 50 = 400 Substitute 10 for t and simplify. ANSWER The total cost for 10 hours of studio time is $400.

Guided Practice WHAT IF? In Example 5, suppose the recording studio raises its initial fee to $75 and charges $40 per hour for studio time. 6. Write an equation that gives the total cost of an album as a function of studio time (in hours). a. C = 40t +75 ANSWER Find the total cost of recording an album that takes 10 hours of studio time. b. $475 ANSWER

Lesson Quiz Write an equation of the line with a slope of –4 and a y-intercept of 1. 1. ANSWER y = –4x + 1 Write an equation of the line that passes through the given points. (–9, 1), (0, –8) 2. ANSWER y = –x – 8 (–4, –6), (0, 6) 3. ANSWER y = 3x + 6

Lesson Quiz Write an equation for the linear function f with f(0) = –4 and f(–1) = –9. 4. ANSWER y = 5x – 4 An electronics game store sells used games for $12.99 with a $20 membership fee. Write an equation that gives the total cost to become a member and buy games as a function of the number of games that are purchased. Then find the cost for 6 games. 5. ANSWER C = 12.99g + 20 where C is total cost and g is the number of games; $97.94