Answered

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

\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Mia's Work} \\
\hline
Step 1 & \(\frac{3-35}{10-91}\) \\
\hline
Step 2 & \(\frac{-32}{-81}\) \\
\hline
Step 3 & \(\frac{32}{81}\) \\
\hline
\end{tabular}

What was the first error that Mia made?

A. Mia simplified incorrectly and made the slope positive.
B. Mia subtracted in the wrong order.
C. Mia switched the numerator and the denominator.
D. Mia used subtraction instead of addition.



Answer :

GinnyAnswer
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]

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