Question

The cost of a pizza is given by the formula $c=-3h+9$, where $c$ and $h$ are the cost of pizza and size of pizza respectively. Determine the $y$-intercept and the $x$-intercept for this given formula for the cost of the pizza.

• A. $y$-intercept is 9 and $x$-intercept is 3.
• B. $y$-intercept is 3 and $x$-intercept is 9.
• C. $y$-intercept is -9 and $x$-intercept is -3.
• D. $y$-intercept is 9 and $x$-intercept is -3.

Answer 1

The correct option is A $y$-intercept is 9 and $x$-intercept is 3.

Given, $c=-3h+9$
We can represent cost of pizza$\left(c\right)$ on $y$-axis and size of pizza $\left(h\right)$ on $x$-axis.
Hence, we can treat $c$ as $y$ and $h$ as $x$.

Step 1: To determine the $y$-intercept, put $x=0$ i.e $h=0$ in the equation $c=-3h+9$
$c=-3\times 0+9$
$c=9$
So the $y$-intercept is 9 and the point is $(0,9).$

Step 2: To determine the $x$-intercept, put $y=0$ i.e $c=0$ in the equation $c=-3h+9$
$0=-3h+9$
$-9=-3h$
$\frac{-9}{-3}=h$
$h=3$
So the $x$-intercept is 3 and the point is $(3,0).$

Step 3: Join the points $(0,9)$ and $(3,0)$ to get the line.
Hence, $y$-intercept is 9 and $x$-intercept is 3.
Option (a) is correct.