Question

for each graph, determine whether x and y are proportional.
if x and y are proportional, fill in the blank with a number in simplest form.
(a) determine whether x and y are proportional.
☐ proportional
$y$ is $\square$ times $x$
☐ not proportional
(b) determine whether x and y are proportional.
☐ proportional
$y$ is $\square$ times $x$
☐ not proportional

Explanation:

Step1: Check proportionality for (a)

Proportional graphs pass through (0,0) and have a constant $\frac{y}{x}$. The first graph passes through (0,0), (4,3), (8,6).
Calculate $\frac{y}{x}$ for (4,3): $\frac{3}{4}$
Calculate $\frac{y}{x}$ for (8,6): $\frac{6}{8}=\frac{3}{4}$

Step2: Confirm proportionality for (a)

The ratio $\frac{y}{x}$ is constant, so $y=\frac{3}{4}x$.

Step3: Check proportionality for (b)

Proportional graphs must pass through (0,0). The second graph passes through (0,5), not (0,0).

Answer:

(a) Proportional, $y$ is $\frac{3}{4}$ times $x$
(b) Not proportional