Question

Please help me with my homework!

Answer 1

The machine makes 45 bottles per minute.

Explanation:

We can first find the slope through this equation:
`(y2-y1)/(x2-x1)`

Since we are given two points, (2,90) and (7,315), we can plug those two points into the formula given above:

`(315-90)/(7-2)`

= 45

Therefore, m = 45.

Now, we can pick one of the two points given--in this case, I'll use (2,90)--to find the equation of the line:
`y-y1 = m(x-x1)`

For (2,90), y1 will be 90, and x1 will be 2. Let's also plug in m:

y - (90) = 45(x - 2)

We can solve for y now to find what y=mx+b is:

y = 45(x-2) + 90

y = 45x

Since the problem asks how many bottles the machine can make per minute, we can plug x = 1: 45(1) = 45

The machine makes 45 bottles per minute.