Lorena calculated the slope of the linear function that is represented by the table of values as shown.

Question

x
y
–10
15
–8
27
–6
39
–4
51
–2
63

m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction = StartFraction 63 minus 51 Over negative 2 minus (negative 4) EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2.

What did she do wrong?
She used the wrong formula for slope.
She used the wrong points to determine the slope.
She made a mistake when she subtracted x 1 from x 2.
She made a mistake when she subtracted y 1 from y 2.

Answer 1

Lorena's calculation of the slope of the linear function seems correct when we analyze the values she used. The correct points she should have used are \((-4, 51)\) for \((x_1, y_1)\) and \((-2, 63)\) for \((x_2, y_2)\).

Calculating the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{63 - 51}{-2 - (-4)} = \frac{12}{-2} = -6 \]

Lorena calculated the slope correctly based on the points she selected, but she did not choose the points in the correct order for subtraction which may have led to an incorrect sign in her final result.

Thus, the issue is: She used the wrong points to determine the slope.

Specifically, she should have chosen \((-4, 51)\) for \(y_1\) and \((-2, 63)\) for \(y_2\) with correct values for \(x_1\) and \(x_2\).