What you’ll learn
Write y = kx.
Key idea
Find k by dividing an output by its matching input. Then replace k with the calculated rate and define what x and y represent.
Substitute a second pair into the equation as a check. If the input is zero, the output must also be zero. A rule such as y = kx + b with nonzero b describes a linear relationship, but not a proportional one.
Worked example
Enter the exact value or ordered values in the format requested below.
Notebooks cost $4 each, no fixed fee; a purchase of 3 costs $12. Let x be notebook count and y dollars. Write the proportional equation y=kx.
- With no fixed fee, zero notebooks cost zero and x notebooks cost 4x dollars.
- Thus y=4x; at x=3, y=12, confirming the no-fee model.
Answer: y=4x
Quick Check
Choose which candidate representation satisfies the requirements of 'Write y = kx' and justify the choice.
A no-fee notebook table lists (0,0),(1,7),(7,49). Select the equation meeting every row with x notebooks,y dollars.