Question

Interpreting a Prediction
A graph has average temperature (degrees Fahrenheit) on the x-axis, from 0 to 60, and total coat sales on the y-axis, from 0 to 100. A trend line goes through points (55, 50) and (65, 40).

Quincy claims that if 80 coats are sold, the outside temperature is likely to be about 42°F. Did Quincy make a reliable prediction? If not, what was his mistake?
Yes. Quincy’s prediction is reliable.
No. Quincy should have used the trend line to find the corresponding y value when x=80.
No. Quincy should have used the trend line to find the corresponding x value when y=80.
No. The prediction is extrapolated, so it is too far off the graph to be reliable.

Answer 1

No. Quincy should have used the trend line to find the x-value when y = 80.

From the two points (55,50) and (65,40) the line is y = −x + 105.
Setting y = 80 gives 80 = −x + 105 ⇒ x = 25. So the trend line predicts about 25°F, not 42°F.