Let's analyze Mia's steps carefully.
We are trying to find the slope of the trend line through the points \((3, 10)\) and \((35, 91)\). The slope formula is given by:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\[ (x_1, y_1) = (3, 10) \][/tex]
[tex]\[ (x_2, y_2) = (35, 91) \][/tex]
Following this formula, we should calculate:
[tex]\[ \text{slope} = \frac{91 - 10}{35 - 3} \][/tex]
Calculating the differences:
[tex]\[ y_2 - y_1 = 91 - 10 = 81 \][/tex]
[tex]\[ x_2 - x_1 = 35 - 3 = 32 \][/tex]
Thus, the correct slope calculation should be:
[tex]\[ \text{slope} = \frac{81}{32} \][/tex]
Now, let's look at Mia's steps:
Step 1: \(\frac{3 - 35}{10 - 91}\)
This step results in:
[tex]\[ \frac{3 - 35}{10 - 91} = \frac{-32}{-81} \][/tex]
Step 2: \(\frac{-32}{-81}\) simplifies to:
[tex]\[ \frac{32}{81} \][/tex]
In these steps, it is clear that Mia has subtracted in the order \(\frac{x_1 - x_2}{y_1 - y_2}\) instead of the correct denominator-over-numerator order \(\frac{y_2 - y_1}{x_2 - x_1}\). This means she subtracted the coordinates in the wrong order.
Thus, the first error Mia made was:
[tex]\[ \text{Mia subtracted in the wrong order.} \][/tex]
So the correct choice is:
[tex]\[ \text{Mia subtracted in the wrong order.} \][/tex]
