Question

the graph shows the relationship between the time in minutes and the number of milk cartons that machine 1 can fill. the equation y = 22x describes the rate at which machine 2 can fill cartons where x is the number of minutes and y is the number of cartons filled. answer parts a and b.
a. what is the unit rate for each machine?
machine 1s unit rate is □ cartons per minute
milk cartons filled

Explanation:

Step1: Find unit - rate for Machine 2

The equation for Machine 2 is $y = 22x$, where $y$ is the number of cartons and $x$ is the number of minutes. The unit - rate is the coefficient of $x$. So, the unit rate for Machine 2 is 22 cartons per minute.

Step2: Find unit - rate for Machine 1 from the graph

Pick two points on the line of Machine 1's graph, say $(2,50)$ and $(6,150)$. The unit rate (slope) $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{150 - 50}{6 - 2}=\frac{100}{4}=25$ cartons per minute.

Answer:

Machine 1: 25 cartons per minute
Machine 2: 22 cartons per minute