Question

circle all that apply.
if two sets of data are proportional to one another:
a. the value of every ratio $\frac{y}{x}$ will not be equal.
b. the graph that represents the data will be a straight line passing through the origin.
c. the graph will contain the points $(0,0)$ and $(1,r)$ where $r$ is the unit rate.
d. there will exist a constant, $k$, for which you can replace in the equation $y = kx$.

Explanation:

• For two proportional data sets, the ratio \(\frac{y}{x}\) is constant (so option a is wrong).
• The equation is \(y = kx\) (option d is correct).
• When \(x = 0\), \(y=0\); when \(x = 1\), \(y = k\) (unit rate \(r = k\), so option c is correct).
• The graph of \(y=kx\) is a straight - line through the origin (option b is correct).

Answer:

b. the graph that represents the data will be a straight line passing through the origin.
c. the graph will contain the points \((0,0)\) and \((1,r)\) where \(r\) is the unit rate.
d. there will exist a constant, \(k\), for which you can replace in the equation \(y = kx\).