Question

Calculate the slope of a line that is perpendicular to the one shown in the graph.(1 point)
m=
points : (0,6) (3,0)

Answer 1

To find the slope of a line that is perpendicular to the one represented by 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:

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

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

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

We can plug in these values:

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

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

To find the slope of a line that is perpendicular to this line, we take the negative reciprocal of the original slope. The negative reciprocal of \( -2 \) is:

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

Therefore, the slope of the line that is perpendicular to the given line is:

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