Question

The graph below shows the proportional relationship between the number of pizzas Amelia makes and the time it takes her to make the pizzas. Find the number of pizzas Amelia can make in 3 hours.

Answer 1

Let's find the equation of the line.

The equation of a line is found by the formula

`y-y_1=m(x-x_1)`

Where

m is the slope (rise over run)

(x_1, y_1) is a point through which the line passes

The slope can be found just by looking at the graph. We take any 2 points and find the change in y coordinates and divide it by the change in x coordinates.

Let's take (0,0) and (1, 5).

We can see that the change in y coordinates is 5 and the change in x coordinates is 1. Thus, the slope is 5/1 = 5

So, we have

`\begin{gathered} m=5 \\ (x_1,y_1)=(0,0) \end{gathered}`

Let's use the formula and find out the equation of the line:

`\begin{gathered} y-y_1=m(x-x_1) \\ y-0=5(x-0) \\ y=5(x) \\ y=5x \end{gathered}`

Now, we want to find the number of pizzas (y) Amelia can make in 3 hours (x). We simply plug in "3" into x and solve for y. This is shown below:

`\begin{gathered} y=5x \\ y=5(3) \\ y=15 \end{gathered}`

So, Amelia can make 15 pizzas in 3 hours.

Answer

15 pizzas