The graph below shows the relation between a cost of a party and the number of people attending. Determine the rate of change.
In order to find the rate of change, we need to take the change in the 𝑦-values and divide by the change in the 𝑥-values. Our 𝑦-values represent the total cost. So we can replace 𝑦-values with total cost. And then, our 𝑥-values represent the number of people. So now, in order to find that change, we need to pick two points that are on the graph that are very clear to us.
Here will be one and the next one that goes exactly through the grid will be here. So this is the point four, 100 and this is the point 12, 250. So first of all, what all of these mean? Four, 100, so four represents the number of people and 100 represents the total cost. So if there’ll be a party of four people, it would cost 100 dollars.
Now, for our other point, it’s saying that if we had a party of 12 people attending, it would cost 250 dollars. So let’s begin with the change in the total cost. How much did we change from 100 to 250? We can find that by subtracting them. So we take 250 and subtract 100. And now for the number of people, we went from four to 12. So to find that change or difference, we take 12 minus four. 250 minus 100 is 150 and 12 minus four is eight.
Now, we need to reduce this because a rate of change should always be simplified. We can divide both of these numbers by two and we get seventy-five fourths. So seventy-five fourths is our final answer. And it means that for every four people that are attending, we will need to add 75 dollars to our total cost.