Grade 7 · Unit 1 · Lesson 5 · part 2 of 5
One short sentence
A proportional relationship always multiplies by the same number, the unit rate.
One short sentence
A proportional relationship always multiplies by the same number, the unit rate.
If that is true, we can write it in one short math sentence:
y = rx
Read it as the output equals the unit rate times the input. y is the output, x is the input, and r is the unit rate, the constant of proportionality, the number that never changes. The letters sit next to each other, rx, and that means multiply: r times x.
EquationA math sentence with an equals sign.
VariableA letter that stands for an amount that can change, like x or y.
rThe unit rate. The only number in the equation, and it never changes.
You can use letters that match the story. Gas costs $3.20 a gallon. Let c be the cost and g be the gallons:
c = 3.20g
Cost equals 3.20 times gallons. Same shape as y = rx, with r = 3.20.