Grade 7 · Unit 1 · Lesson 5

Writing y = rx

If a relationship always multiplies by the same number, you can say so in one short sentence: y = rx, the output equals the unit rate times the input. Use letters that match the story, use the equation forward and backward, and find r from a table, a graph, or words.

About 25 minutes Output = unit rate × input

ElleMath-speak

I say it the way your test says it.

FinnPlain English

And I say it the way you would say it to a friend. Same idea, two ways.

Finn

Today we squeeze a whole table into one short equation.

The big idea

Finn says

A proportional relationship always multiplies by the same number, the unit rate.

A proportional relationship always multiplies by the same number, the unit rate. Written as an equation, that is y = rx: the output equals the unit rate times the input. r is the unit rate, the constant of proportionality, and it is the only number in the equation. Use letters that match the story, like c = 3.20g. Multiply by r to go from input to output, and divide by r to go back. To write the equation, find r in a table (divide), on a graph (read the point at an input of 1), or in the words, then put it next to x. Every relationship can be written two ways, and the story decides which one is useful.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2One short sentenceA proportional relationship always multiplies by the same number, the unit rate. 3Forward and backwardThe equation works in both directions. 4Find r, then write itTo write the equation, find r, then write y = rx with that number. 5Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with y = rx read in plain English, forward and backward, the four places to find r, and the bus driver. Plus a worksheet with an answer key and a short lesson plan for the parent or tutor.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Proportional GraphsA straight line through zero. Next lesson: What a Point MeansReading any point, plus (0, 0) and (1, r). Back to the Math 7 mapEvery 7th grade lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.

NC Grade 7 standards in this lesson: NC.7.RP.2.