Question

(0,6)
(3,0)

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

m = ___

Answer 1

To find the slope of a line that is perpendicular to the line defined by the points (0, 6) and (3, 0), we first need to find the slope of the line passing through those points.

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

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

For the points \( (0, 6) \) and \( (3, 0) \):

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

Now substituting these values into the slope formula:

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

The slope of the line through those points is \( -2 \).

To find the slope of a line that is perpendicular to this line, we use the fact that the slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the original line is \( m = -2 \), the slope of a line that is perpendicular to it is:

\[
m_{\perpendicular} = -\frac{1}{m} = -\frac{1}{-2} = \frac{1}{2}
\]

Thus, the slope \( m \) of the line that is perpendicular to the given line is:

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

So, \( m = \frac{1}{2} \).