Question

each graph, determine whether x and y are proportional. if x and y are proportional, fill in the blank with a number. graph 1 graph of a line through (0,0), (1,1), (2,2) proportional y is blank times x not proportional graph 2 graph of a line through (0,0), (1,3), (2,6) proportional y is blank times x not proportional

Explanation:

Step1: Check Graph 1 proportionality

Proportional graphs pass through (0,0) and have constant $\frac{y}{x}$.
For Graph 1: points are (0,0), (1,1), (2,2), (12,12).
$\frac{1}{1}=1$, $\frac{2}{2}=1$, $\frac{12}{12}=1$. Constant ratio, passes through origin.

Step2: Find Graph 1 scaling factor

$y = kx$, $k=\frac{y}{x}=1$.

Step3: Check Graph 2 proportionality

Graph 2 passes through (0,0), (1,3), (2,6).
$\frac{3}{1}=3$, $\frac{6}{2}=3$. Constant ratio, passes through origin.

Step4: Find Graph 2 scaling factor

$y = kx$, $k=\frac{y}{x}=3$.

Answer:

Graph 1: Proportional, $y$ is $\boldsymbol{1}$ times $x$
Graph 2: Proportional, $y$ is $\boldsymbol{3}$ times $x$