M4.2.6 For the adult
Proportion as a formula
If y is proportional to x, how do I write that as a formula?
What this chapter teaches
Direct proportion is y = kx for a fixed number k, found by dividing y by x for one pair. Proportion to x² is y = kx², and doubling x makes y four times as big. Inverse proportion is y = k ÷ x, where x times y stays fixed.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you find k when you know one pair of values of x and y?
- If y is proportional to x², what happens to y when x is doubled?
- What stays the same in inverse proportion when x goes up?
After the chapter, the learner can
- Write y = kx for direct proportion and find k
- Solve problems where y is proportional to x² or to 1/x
What they copy into their notebook
Proportional to x: y = kx, and y ÷ x is always k. Proportional to x²: y = kx². Inversely proportional to x: y = k ÷ x, and x times y is always k.