Marisol attempted to determine the slope of a line based on the two points shown in the table below.

x
y
–1
4
3
10

Step 1: (–1, 4) and (3, 10)

Step 2: StartFraction 10 minus 3 Over 4 minus (negative 1) EndFraction

Step 3: StartFraction 7 Over 5 EndFraction

Which statement best explains Marisol’s error?
Marisol computed StartFraction y 2 minus y 1 Over x 1 minus x 2 EndFraction.
Marisol computed StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction.
Marisol computed StartFraction y 2 minus x 2 Over y 1 minus x 1 EndFraction.
Marisol computed StartFraction x 2 minus y 2 Over x 1 minus y 1 EndFraction.

1 answer

Marisol calculated the slope incorrectly in Step 2. The correct formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

In the provided steps, Marisol labeled the points as \((x_1, y_1) = (-1, 4)\) and \((x_2, y_2) = (3, 10)\). Therefore, \((x_1, y_1)\) yields \(y_1 = 4\) and \(x_1 = -1\) while \((x_2, y_2)\) gives \(y_2 = 10\) and \(x_2 = 3\).

However, in her calculation, she used:

\[ \frac{10 - 3}{4 - (-1)} = \frac{7}{5} \]

This suggests that she took \(y_2 - y_1\) correctly as \(10 - 4 = 6\) and added to it \(y_1 - x_1\) incorrectly on the bottom rather than calculating \(x_2 - x_1\) as \(3 - (-1) = 4\).

Marisol actually computed:

\[ \frac{y_2 - y_1}{y_1 - x_1} \]

instead of the correct slope calculation.

The correct implication is:

Marisol computed \(\frac{y_2 - y_1}{x_2 - x_1}\) correctly for \(y\) values but incorrectly handled the \(x\) values. This fits with the statement that says:

"Marisol computed \(\frac{y_2 - x_2}{y_1 - x_1}\)."

Thus, the best option explaining her error is:

Marisol computed \(\frac{y_2 - x_2}{y_1 - x_1}\).