Question

What is the slope perpendicular to the line

5x-10y=20

a
1/2

b
2

c
-2

d
-3/2

Answer 1

To find the slope of the line perpendicular to the given line \( 5x - 10y = 20 \), we first need to determine the slope of the original line.

1. **Rearrange the equation into slope-intercept form (y = mx + b):**

Start with the equation:
\[
5x - 10y = 20
\]

Subtract \( 5x \) from both sides:
\[
-10y = -5x + 20
\]

Divide every term by \(-10\):
\[
y = \frac{1}{2}x - 2
\]

From this, we can see that the slope \( m \) of the line is \( \frac{1}{2} \).

2. **Find the slope of the perpendicular line.**

The slope of a line that is perpendicular to another is the negative reciprocal of the slope of the original line. The reciprocal of \( \frac{1}{2} \) is \( 2 \), and the negative of that is:
\[
-2
\]

So, the slope perpendicular to the line \( 5x - 10y = 20 \) is \(-2\).

Thus, the correct answer is:
**c) -2**.