Question

Use the image to answer the question.

A coordinate plane shows two plots in the second and fourth quadrants joined by a line.

Image Long DescriptionThe x and y axes range from negative 8 to 8 in 1-unit increments. The plots are marked and labeled at left parenthesis negative 4 comma 5 right parenthesis and left parenthesis 8 comma negative 1 right parenthesis. Both the plots are connected by a solid diagonal line.

Calculate the slope of the line based on the two points in the graph. Leave the answer in simplest fraction form, if it applies. If the slope is undefined, enter a value of 100.

(1 point)
The slope of the line is
.

Answer 1

To calculate the slope of the line that connects the two points \((-4, 5)\) and \((8, -1)\), we use the formula for the slope \(m\):

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

where \((x_1, y_1) = (-4, 5)\) and \((x_2, y_2) = (8, -1)\).

Plugging the values into the formula:

\[
m = \frac{-1 - 5}{8 - (-4)}
\]
\[
m = \frac{-6}{8 + 4}
\]
\[
m = \frac{-6}{12}
\]
\[
m = -\frac{1}{2}
\]

Thus, the slope of the line is

\[
\boxed{-\frac{1}{2}}.
\]