A table shows (x=1, y=3), (x=2, y=6), (x=3, y=10). Does this table represent a proportional relationship?
AYes, because most of the ratios equal 3
BNo, because the ratios y/x are not all equal
CYes, because the y-values are increasing
DNo, because the table does not start at (0, 0)
For a proportional relationship, every y/x ratio must be the same. Here 3/1 = 3 and 6/2 = 3, but 10/3 ≈ 3.33 — not equal. Checking only the first pair is the classic error this question targets.
Question 2 True / False
Any straight-line graph represents a proportional relationship between the two quantities.
TTrue
FFalse
Answer: False
A proportional relationship requires the graph to be a straight line that passes through the origin (0, 0). A line like y = 2x + 1 is linear but NOT proportional because it has a y-intercept of 1, meaning the ratio y/x is not constant.
Question 3 Short Answer
What is the constant of proportionality in y = kx, and how do you find it from a table of values?
Think about your answer, then reveal below.
Model answer: The constant of proportionality k is the unit rate — the value y/x. To find it from a table, divide any y-value by its corresponding x-value. If the relationship is truly proportional, every pair gives the same quotient.
k captures the rate at which y changes per unit of x. Because y = kx, rearranging gives k = y/x. The key insight is that k must be consistent across all rows; if it is not, the relationship is not proportional.