To find the slope of the line that passes through the points \( (4, 24) \) and \( (16, 18) \), we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \( (x_1, y_1) = (4, 24) \) and \( (x_2, y_2) = (16, 18) \).
Substituting in the values:
\[ m = \frac{18 - 24}{16 - 4} = \frac{-6}{12} = -\frac{1}{2} \]
Willa claimed the slope is negative one-third \((- \frac{1}{3})\), which is incorrect. She miscalculated the slope.
Looking at the error options provided:
- The slope is positive instead of negative. - This is false; the slope is indeed negative.
- She counted the squares instead of using the scale. - Counting squares is not relevant here; the calculation can be done with the coordinates directly.
- She used the points that are further apart instead of the two consecutive points. - This is incorrect because the correct points were used.
- She used StartFraction rise Over run EndFraction when finding slope. - This is misleading; the formula for slope \(\frac{\text{rise}}{\text{run}}\) is correct, but she made an error in computing the actual values.
Given the answer choices, the best option is that Willa made an arithmetic error in her calculation of the slope. Since none of the options directly point out her calculation issue correctly, you can state that she miscalculated the slope.
But in context, if you need a direct match from the options, the first one could be misleadingly interpreted as correct due to the sign, but knowing the slope is \(-\frac{1}{2}\), her answer cannot be considered strictly under these options. The best conclusion considering the context is to simply note that her calculated slope was a miscalculation, but none of the error descriptions adequately captures the precise mistake she made.
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