A student finds the slope of the line between (14, 1) and (18, 17). She writes . What mistake did she make?

Question

She did not keep the order of the points the same in the numerator and the denominator.

She should have added the values, not subtracted them.

She mixed up the x- and y-values.

She used y-values where she should have used x-values.

Answer 1

To find the slope of the line between two points \((x_1, y_1)\) and \((x_2, y_2)\), the formula used is:

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

In this case, the points are \((14, 1)\) and \((18, 17)\). Let's assign the values:

• \((x_1, y_1) = (14, 1)\)
• \((x_2, y_2) = (18, 17)\)

Applying the formula:

\[ \text{slope} = \frac{17 - 1}{18 - 14} = \frac{16}{4} = 4 \]

Now, let's analyze the possible mistakes stated:

1. She did not keep the order of the points the same in the numerator and the denominator.

   • This could lead to a negative slope if the points are switched improperly.

2. She should have added the values, not subtracted them.

   • This is incorrect since the calculation of the slope does require subtraction.

3. She mixed up the x- and y-values.

   • This would lead to an incorrect calculation.

4. She used y-values where she should have used x-values.

   • This also signifies a serious error in understanding the slope formula.

Given these options, the most critical mistake commonly made is:

She did not keep the order of points the same in the numerator and the denominator.

This implies that the student might have calculated something like \(\frac{y_1 - y_2}{x_1 - x_2}\), which could yield an incorrect slope value.