What you’ll learn
Find constant of proportionality.
Key idea
From a nonzero pair, calculate k = y/x. If a table has several pairs, the same quotient should appear each time. In a graph, k is the slope of a proportional line through the origin.
Name the units in the same order as the quantities in y/x. If y is cost in dollars and x is kilograms, k is dollars per kilogram. Do not divide x by y unless the question asks for the reciprocal rate.
Worked example
Enter the exact value or ordered values in the format requested below.
A proportional rule y=kx includes point (8,16/5). Enter exact numerical k.
- For y=kx and nonzero x=8, k=y/x=(16/5)/8=2/5.
- The inverse input equation y/k=x checks 16/5/(2/5)=8.
Answer: 2/5
Quick Check
Evaluate a worked attempt at find constant of proportionality, identify the first invalid step, and provide the correction.
A student finds k through (6,9/2): Step 1: k=y/x. Step 2: k=6/(9/2)=4/3. Locate the first invalid step and correct k.