Question

Calculate the slope of a line that is perpendicular to the one shown in the graph.
First Point: (0, 6)
Second Point: (3, 0)

Answer 1

To calculate 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 through those points.

The slope \( m \) of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

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

Plugging in the given points:

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

Calculating the slope:

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

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

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

1. The reciprocal of \(-2\) is \(-\frac{1}{2}\).
2. The negative of that reciprocal is \( \frac{1}{2} \).

Therefore, the slope of the line that is perpendicular to the line through the points (0, 6) and (3, 0) is:

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