Grade 7 · Unit 1 · Lesson 5 · part 4 of 5

Find r, then write it

To write the equation, find r, then write y = rx with that number.

Find r, then write it

To write the equation, find r, then write y = rx with that number. You can find r in all four places now.

From a table

2 hours $16, 5 hours $40. Divide: 16 ÷ 2 = 8. y = 8x.

From a graph

Go over to an input of 1 and read up. The line is at 0.75. y = 0.75x.

From words

Tickets cost $7.50 each. c = 7.50t.

From an equation

y = 35x. The unit rate is the number next to x: 35.

The bus driver. A bus driver's afternoon drive takes 1.5 times as long as the morning drive. If the morning drive takes m minutes, the afternoon takes 1.5m, and the whole day is the morning plus the afternoon: m + 1.5m = 2.5m. So the total time is

t = 2.5m

The unit rate is 2.5: every 1 minute of morning driving means 2.5 minutes for the whole day. A 40-minute morning makes a 2.5 × 40 = 100-minute day.

Two ways to write it Every ratio has two unit rates, so every relationship can be written two ways. Gas: c = 3.20g (cost for each gallon) or g = 0.3125c (gallons for each dollar). The story decides which one is useful. If you are filling a tank and want the cost, use the first.

Where to go next