Question

Calculate the slope of a line that is perpendicular to the one shown in the graph.
0, 6
3, 0

Answer 1

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

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

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

Using the points (0, 6) and (3, 0):

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

Now we calculate the slope:

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

The slope of the line between the points (0, 6) and (3, 0) is \(-2\).

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. To find the slope \( m_{\text{perpendicular}} \) of the line that is perpendicular to the one we just found, we take the negative reciprocal of \(-2\):

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

Therefore, the slope of the line that is perpendicular to the one shown in the graph is \(\frac{1}{2}\).