5.1
Write Linear Equations in Slope-Intercept Form
Warm Up
Lesson Presentation
Lesson Quiz
5.1
Warm-Up
Find the slope of the line that passes through the points.
1. (2, –1), (4, 0)
ANSWER
1
2
2. (–1, –3), (1, 5)
ANSWER
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
Write an equation of the line with the given slope
and y-intercept.
1.
Slope is 8; y-intercept is –7.
ANSWER
2.
y = 8x – 7
Slope is 3 ; y intercept is –3.
4
3x–3
ANSWER
y= 4
5.1
Example 2
Which equation represents the line shown?
2
B y = – 5x + 3
y=– x+3
A
5
2
C
y=–
2
x+1
5
D
2
y = 3x + 5
The slope of the line is rise = –2 = – 2 .
run
5
5
The line crosses the y-axis at (0, 3). So, the
y-intercept is 3.
Write slope-intercept form.
y = mx + b
y=– 2 x+3
5
Substitute – 2 for m and 3 for b.
5
5.1
Example 2
ANSWER
The correct answer is A. A
B
C
D
5.1
Example 3
Write an equation of the
line shown.
SOLUTION
STEP 1 Calculate the slope.
y2 – y1
–1 – (–5)
4
m = x –x =
=
3–0
2
1
3
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
y= 4 x–5
3
Write slope-intercept form.
Substitute 4 for m and 5 for b.
3
5.1
3.
Guided Practice
Write an equation of the line shown.
ANSWER
y=– 1 x+1
2
5.1
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).
y2 – y1
m=
x2 – x1 =
17 – 5
4–0
12
= 4 =3
5.1
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.
5.1
Guided Practice
Write an equation for the linear function f with the
given values.
4. f(0) = –2, f(8) = 4
ANSWER
y= 3 x–2
4
5. f(–3) = 6, f(0) = 5
ANSWER
y = – 13 x + 5
5.1
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.
a.
Write an equation that gives the total cost of
an album as a function of studio time (in
hours).
b.
Find the total cost of recording an album that
takes 10 hours of studio time.
5.1
Example 5
SOLUTION
a.
The cost changes at a constant rate, so you can
write an equation in slope-intercept form to model
the total cost.
STEP 1
Identify the rate of change and the starting value.
Rate of change, m: cost per hour
Starting value, b: initial fee
5.1
Example 5
STEP 2
Write a verbal model. Then write the equation.
C
=
35
t
+
50
CHECK
Use unit analysis to check the equation.
dollars = dollars hours + dollars
hour
ANSWER
The total cost C is given by the function
C = 35t + 50 where t is the studio time (in hours).
5.1
b.
Example 5
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.
5.1
6.
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.
a.
Write an equation that gives the total cost
of an album as a function of studio time
(in hours).
ANSWER
b.
C = 40t +75
Find the total cost of recording an
album that takes 10 hours of studio time.
ANSWER
$475
5.1
1.
Lesson Quiz
Write an equation of the line with a slope of –4 and
a y-intercept of 1.
ANSWER
y = –4x + 1
Write an equation of the line that passes through the
given points.
2.
(–9, 1), (0, –8)
ANSWER
3.
y = –x – 8
(–4, –6), (0, 6)
ANSWER
y = 3x + 6
5.1
4.
Lesson Quiz
Write an equation for the linear function f with
f(0) = –4 and f(–1) = –9.
ANSWER
5.
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.
ANSWER
C = 12.99g + 20 where C is total cost and g is the
number of games; $97.94