Question

Andrea’s work to find the equation of a trend line through the points (48, 61) and (72, 195) is shown below.

Andrea’s Work


Step 1
m = StartFraction 72 minus 48 Over 195 minus 61 EndFraction = StartFraction 24 Over 134 EndFraction = StartFraction 12 Over 67 EndFraction
Step 2
61 = (StartFraction 12 Over 67 EndFraction) (48) + b
Step 3
b = StartFraction 3,511 Over 67 EndFraction
Step 4
y = StartFraction 12 Over 67 EndFraction x + StartFraction 3,511 Over 67 EndFraction

What was the first error that Andrea made?
Andrea used the reciprocal of the slope.
Andrea made a computational error when she simplified m.
Andrea substituted incorrectly when she solved for b.
Andrea made a sign error when she solved for b.

Answer 1

Andrea used the reciprocal of the slope.

The correct slope is (195−61)/(72−48) = 134/24 = 67/12, but Andrea computed 24/134 = 12/67, which is the reciprocal.