Question

What is the slope of a line that is perpendicular to a line whose equation is 5y=10+2x?

Enter your answer in the box.

Answer 1

To find the slope of a line that is perpendicular to the line given by the equation \( 5y = 10 + 2x \), we first need to determine the slope of the original line.

1. **Rearranging the equation into slope-intercept form (y = mx + b)**:
\[
5y = 10 + 2x
\]
Divide all terms by 5:
\[
y = \frac{2}{5}x + 2
\]

In this equation, the coefficient of \( x \) represents the slope (m) of the line.

The slope of the line is:
\[
m = \frac{2}{5}
\]

2. **Finding the slope of the perpendicular line**:
The slope of a line that is perpendicular to another is the negative reciprocal of the original slope. Therefore, we take the reciprocal of \( \frac{2}{5} \) and then change the sign.

The reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \), and the negative reciprocal would be:
\[
-\frac{5}{2}
\]

Thus, the slope of the line that is perpendicular to the original line is:
\[
\boxed{-\frac{5}{2}}
\]