5.1

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Write Linear Equations in Slope-Intercept Form

5.1 Warm-Up

Find the slope of the line that passes through the points.

2. (–1, –3), (1, 5)

ANSWER

ANSWER

1. (2, –1), (4, 0)

12

4

5.1 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

5.1 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.

5.1 Guided Practice

1. Slope is 8; y-intercept is –7.

Write an equation of the line with the given slope and y-intercept.

y = 8x – 7 ANSWER

2. Slope is ; y intercept is –3. 34

y = 34

x – 3ANSWER

5.1 Example 2

Which equation represents the line shown?

The line crosses the y-axis at (0, 3). So, the y-intercept is 3.

y = mx + b Write slope-intercept form.

2y = – x + 35

2Substitute – for m and 3 for b.5

= = –The slope of the line is riserun

–2 5

25

.

A y = – x + 325 B y = – x + 35

2

C y = – x + 125 D y = 3x +

25

5.1 Example 2

ANSWER

The correct answer is A. B DCA

5.1 Example 3

Write an equation of the line shown.

y = mx + b

y = x – 543

Substitute for m and 5 for b.43

STEP 1

Write an equation of the line. The line crosses the y-axis at (0, –5). So, the y-intercept is –5.

SOLUTION

x2 – x1 33 – 0y2 – y1=m =

–1 – (–5)=

4

Write slope-intercept form.

Calculate the slope.

STEP 2

5.1 Guided Practice

3. Write an equation of the line shown.

2 1 x + 1y =ANSWER –

5.1 Example 4

SOLUTION

Write an equation for the linear function f with the values f(0) = 5 and f(4) = 17.

Calculate the slope of the line that passes through (0, 5) and (4, 17).

Write f(0) = 5 as (0, 5) and f (4) = 17 as (4, 17).STEP 1

x2 – x1 4 – 0y2 – y1=m =

17 – 5= 4

12=3

STEP 2

5.1 Example 4

y = mx + b Write slope-intercept form.

y = 3x + 5 Substitute 3 for m and 5 for b.

STEP 3

ANSWER

The function is f(x) = 3x + 5.

5.1 Guided Practice

Write an equation for the linear function f with the given values.

f(0) = –2, f(8) = 4

y = x – 234

ANSWER

f(–3) = 6, f(0) = 5

y = x + 5 13ANSWER –

5.

4.

5.1 Example 5

A recording studio charges musicians an initial fee of $50 to record an album. Studio time costs an additional $35 per hour.

Recording Studio

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.

5.1 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.

Identify the rate of change and the starting value.

Rate of change, m: cost per hour

Starting value, b: initial fee

STEP 1

5.1 Example 5

Write a verbal model. Then write the equation.STEP 2

C = t35 + 50

The total cost C is given by the function C = 35t + 50 where t is the studio time (in hours).

ANSWER

Use unit analysis to check the equation.CHECK

hourdollars = hours + dollarsdollars

5.1 Example 5

Substitute 10 for t and simplify.

b. Evaluate the function for t = 10.

C = 35(10) + 50 = 400

ANSWER

The total cost for 10 hours of studio time is $400.

5.1 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 +75ANSWER

Find the total cost of recording an album that takes 10 hours of studio time.

b.

$475ANSWER

5.1 Lesson Quiz

ANSWER y = –4x + 1

Write an equation of the line with a slope of –4 and a y-intercept of 1.

1.

Write an equation of the line that passes through the given points.

(–9, 1), (0, –8)2.

ANSWER y = –x – 8

ANSWER y = 3x + 6

(–4, –6), (0, 6)3.

5.1 Lesson Quiz

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.

Write an equation for the linear function f with f(0) = –4 and f(–1) = –9.

4.

ANSWER y = 5x – 4

ANSWERC = 12.99g + 20 where C is total cost and g is the number of games; $97.94