Given an equ atio n in slope-intercept form or point-slope form, you can rew rite the
eq u a tio n in stan d ard form using only integers.
How can you get
started?
You need to clear the
fraction. So, multiply
each side of the equation
by the denom inator of
the fraction.
Problem 4 Transforming to Standard Form
What is y = — f x + 5 written in standard form using integers?
3
—| x + 5
y = —yx + 5
7 y =? (
7y = — 3x + 35
3x + 7y = 35
M u ltip ly each side by 7.
Distributive Property
Add 3x to each side.
I d G o t It? 4. Write y - 2 = - | ( x + 6) in stan d ard form using integers.
Using Standard Form as a Model
Online Shopping A media download store sells songs for $1 each and movies
for $12 each. You have $60 to spend. Write and graph an equation that describes
the items you can purchase. What are three combinations of numbers of
songs and movies you can purchase?
Relate cost of times n u m b e r plus , cost of times..
a song ot songs K a movie
number
of equals
movies
$60
Think
Is th e r e a n o th e r w a y
to find solutions?
You can guess and check
by substituting values for
one variable and solving
for the other. Then check
if your solution makes
sense in the context o f
the problem. Graphing is
the quickest w ay to see
all the solutions.
Define Let
Let
Write
x = the n u m b e r of songs p urchased,
y = th e n u m b e r of m ovies p urchased.
1 • X + (^12) y 60
An equ atio n for this situation is x + 12y = 60.
Find the intercepts. 0 songs
5 m o vie s
x + 12y = 60
x + 12(0) = 60
x = 60
x + 12y = 60
0 + 12y = 60
y = 5
Downloads
Use the intercepts to draw th e graph. Only points in the
first q u ad ran t m ake sense.
The intercepts give you two com binations of songs an d
movies. Use th e graph to identify a third com bination.
Each of th e red points is a possible solution.
-Q<u
£ 3
■
24 songs
3 m ovies
3&i 60 songs
0 mn\/ip<;
j
■
12 2 4 3 6 4 8 60
Number of Songs
Check fo r Reasonableness You ca n n o t buy a fraction of a song or movie. The graph is a
line, b u t only points w ith integer coordinates are solutions.
3 2 4 Chapter 5 Lin ear Fu n ct io n s