Cyrus runs on a track at a constant speed of 200 meters per minute. Later, he makes a graph of his run to show his coach. He puts time on the x-axis and distance on the y-axis. A. What points does he plot to show how far he runs in 8 minutes and 12 minutes? Show your work.

We know that Cyrus runs at a constant speed, then we can model this with a linear relationship.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In the graph, we can see two points, and those are:

(0, 0) and (1, 200)

Then the slope of this line will be:

a = (200 - 0)/(1 - 0) = 200

y = 200*x + b

And to find the value of b, we just can replace the values of one of the points in the equation (for example, i will use the point (0,0) ) and get:

0 = 200*0 + b

0 = b

Then the equation is:

y = 200*x

Now we can answer the questions:

What points does he plot to show how far he runs in 8 minutes?

Here we must replace x by 8 in the equation:

y = 200*8 = 1600

Then this point will be (8, 1600)

What points does he plot to show how far he runs in 12 minutes?

Here we must replace x by 12 in the equation:

y = 200*12 = 2400

Then this point will be (12, 2400)