Question

determine whether each equation represents a proportional relationship. if it does, identify the constant of proportionality. explain and show the work in an 7th grader's work.

A. y=0.5x - 2
b. y = 1,000x
c. y = x + 1

Answer 1

A proportional relationship between x and y means y = kx (a straight line through the origin). Two quick tests:
- The equation must have no constant term (y-intercept 0).
- Or plug x = 0: if y = 0 then it might be proportional.

A. y = 0.5x − 2
- Plug x = 0: y = 0.5(0) − 2 = −2, not 0 → not through the origin.
- Try ratios: x = 2 → y = 0.5(2) − 2 = −1, so y/x = −1/2 = −0.5.
x = 4 → y = 0.5(4) − 2 = 0, so y/x = 0/4 = 0. Ratios are not constant.
Answer: Not proportional.

B. y = 1,000x
- This is exactly of the form y = kx with no extra term, so it goes through the origin.
- y/x = 1,000 for any x.
Answer: Proportional. Constant of proportionality k = 1,000.

C. y = x + 1
- Plug x = 0: y = 0 + 1 = 1, not 0 → not through the origin.
- Check ratios: x = 2 → y = 3, y/x = 3/2 = 1.5. x = 4 → y = 5, y/x = 5/4 = 1.25. Ratios change.
Answer: Not proportional.