Question

story 1
story: trinidad earns $12 per hour.
equation: y = 12x
is the relationship proportional?
circle one.
yes
no
explain your thinking.

story 2
story: a recipe recommends 1 banana for every 2 smoothies.
equation: y = \frac{1}{2}x
is the relationship proportional?

Explanation:

Step1: Recall proportional - relationship definition

A relationship $y = kx$ is proportional if $k$ is a non - zero constant and when $x = 0$, $y=0$.

Step2: Analyze Story 1

For the equation $y = 12x$, when $x = 0$, $y=12\times0 = 0$. The ratio of $y$ to $x$ is $\frac{y}{x}=12$ (a non - zero constant). So it is proportional.

Step3: Analyze Story 2

For the equation $y=\frac{1}{2}x$, when $x = 0$, $y=\frac{1}{2}\times0 = 0$. The ratio of $y$ to $x$ is $\frac{y}{x}=\frac{1}{2}$ (a non - zero constant). So it is proportional.

The equation is of the form $y = kx$ ($k = 12$), and when $x = 0$, $y = 0$.
Story 2: Yes

The equation is of the form $y = kx$ ($k=\frac{1}{2}$), and when $x = 0$, $y = 0$.

Answer:

Story 1: Yes