Algebra 1 Common Core Student Edition, Grade 8-9

Direct Variation

@ Com m on C ore State Standards

A-CED.A.2 Cr eat e eq u at i o n s i n t w o o r m o r e v ar i ab l es

to represent relationships between quantities; graph

equat ions on coordinat e axes wit h labels and scales.

Also N-Q.A.2

M P 1, M P 2, M P 3, M P 4, M P 7

Objective To write a n d graph an eq u a tio n of a direct variation

As your distance

fro m lightning

increases, so does

th e tim e it takes

you to hear th e

thunder.

MATHEMATICAL

PRACTICES

|j 'I Getting Ready!

The diagram shows how long it ta k e s to h e a r thunder a f t e r you see

lightning. W h at general rule can you use to model th is situation? Explain.

lesso n

Vocabulary

• direct variation


• constant o f
  variation for a
  direct variation

The tim e it takes to h e a r th u n d e r varies directly w ith th e distance from lightning.

Esse n t i a l U n d e r st a n d i n g If th e ratio of two variables is constant, th e n the

variables have a special relationship, know n as a direct variation.

A direct variation is a relationship th a t can b e re p resen te d by a function in the

form y = kx, where k # 0. The constant of variation for a direct variation k is the

coefficient of x. By dividing each side of y y = kx by x, you can see th a t th e ratio of the

variables is constant: * = k.

To d eterm in e w h e th e r an eq u a tio n rep resen ts a direct variation, solve it for y. If you can

w rite th e eq u a tio n in th e form y = kx, where k + 0, it rep resen ts a direct variation.

Think

Do these equations

look like ones you've

seen before?

Yes. They contain tw o

variables, so they're

literal equations. To

determine whether

they're direct variation

equations, solve fo r y.

Problem 1 Id en tifyin g a Direct V ariatio n

Does the equation represent a direct variation? If so, find the constant of variation.

O 7y = 2x O 3y + 4x = 8

y = 7X^2 *— Solve each equation for y. —> 3y = 8 - 4x

The equation h as th e form y= kx,

so the eq u a tio n is a d irect variation.

Its co n stan t of variation is y.

3X

You ca n n o t w rite th e equation in the form

y = kx. It is n o t a direct variation.

G o t It? 1. D o e s Ax + 5y = 0 represent a direct variation? If so, find the constant of variation.

PowerAlgebra.com j Lesso n 5- 2 Direct Variat io n 301