Question

Use the image to answer the question.

Two points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 7 to 7 in increments of 1. The y-axis ranges from negative 7 to 7 in increments of 1.

Image Long DescriptionThe first point has coordinates left parenthesis 0 comma 6 right parenthesis. The second point has coordinates left parenthesis 3 comma 0 right parenthesis.

Calculate the slope of a line that is perpendicular to the one shown in the graph.

(1 point)
m=

Answer 1

To find the slope of the line that is perpendicular to the line passing through the points \((0, 6)\) and \((3, 0)\), we first need to calculate the slope of the line between those two points.

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting in the coordinates of the points:

- \((x_1, y_1) = (0, 6)\)
- \((x_2, y_2) = (3, 0)\)

This gives us:

\[
m = \frac{0 - 6}{3 - 0} = \frac{-6}{3} = -2
\]

Now that we have the slope of the line between the two points, which is \(-2\), we can find the slope of a line that is perpendicular to this line.

The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Thus, if the original slope is \(m_1 = -2\), the slope \(m_2\) of the perpendicular line is given by:

\[
m_2 = -\frac{1}{m_1} = -\frac{1}{-2} = \frac{1}{2}
\]

Therefore, the slope of the line that is perpendicular to the one shown in the graph is:

\[
m = \frac{1}{2}
\]