Question

Find the slope of a line perpendicular to the graph of each equation.
1.) Y=-x/5 - 7
2.) y = -8

Answer 1

To find the slope of a line perpendicular to the given equations, we first need to identify the slopes of the original lines.

1. For the equation \( Y = -\frac{x}{5} - 7 \):
- The slope (\( m \)) of this line is the coefficient of \( x \), which is \( -\frac{1}{5} \).
- The slope of a line perpendicular to this slope is the negative reciprocal. Therefore:
\[
\text{slope of perpendicular line} = -\frac{1}{(-\frac{1}{5})} = 5
\]

2. For the equation \( y = -8 \):
- This is a horizontal line where the slope is \( 0 \).
- The slope of a line perpendicular to a horizontal line is vertical, which means it is undefined.

In summary:
1. The slope of a line perpendicular to \( Y = -\frac{x}{5} - 7 \) is \( 5 \).
2. The slope of a line perpendicular to \( y = -8 \) is undefined.