Algebra 1 Common Core Student Edition, Grade 8-9

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