Question

a= (0,6)
b= (3,0)
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 a line that is perpendicular to the line that passes through the points \( a = (0,6) \) and \( b = (3,0) \), we first need to calculate the slope of the line connecting these 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 points \( a \) and \( b \):

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

Calculating the slope:

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

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

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

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

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

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