Post on 28-Dec-2015
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 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 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