Mia’s work to find the slope of a trend line through the points (3, 10) and (35, 91) is shown below.

Question

Mia’s Work
Step 1
StartFraction 3 minus 35 Over 10 minus 91 EndFraction
Step 2
StartFraction negative 32 Over negative 81 EndFraction
Step 3
StartFraction 32 Over 81 EndFraction

What was the first error that Mia made?
Mia simplified incorrectly and made the slope positive.
Mia subtracted in the wrong order.
Mia switched the numerator and the denominator.
Mia used subtraction instead of addition.

Answer 1

The first error that Mia made was:

Mia subtracted in the wrong order.

The correct formula for finding the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

In Mia’s work, she subtracted the coordinates in the order of \(3\) minus \(35\) and \(10\) minus \(91\), which is incorrect. She should have used the coordinates as follows:

\[ m = \frac{91 - 10}{35 - 3} \]

This would have produced the correct slope calculation.