Find the linear equation that relates the number of skaters to the temperature

Question

The all weather ice-skating rink has determined that when the temperature is 32°F at 8 AM they can expect 100 skaters in the morning session. For each 5°F rise in temperature, seven fewer skaters will attend the session? Find the linear equation that relates the number of skaters to the temperature. Identify your variables.

Answer 1

First construct a table to look at the information of skaters vs temperature. Use skaters as the independent variable. Let S = Skaters and T = Temperature

Number of skaters Temperature

100 32

93 37

86 42

etc.

If you assume that this is a continuous relationship and has a constant slope, you can model using a line equation. Let's check the slopes.

Compare the first 2 points, the slope m = (100-93)/(32-37) = -7/5

Compare first and last points m = (100-86)/(32-42) = -7/5 OK! (As you would expect)

Then S-100 = -7/5(T-32) or S-100 = (-7/5)T + 224/5 or S = (-7/5)T + 224/5 + 500/5

So, S = (-7/5)T + 724/5