# What is the slope of a line that is perpendicular to the line whose equation is 5 y + 2 x = 12?

## Question:

What is the slope of a line that is perpendicular to the line whose equation is {eq}5 y + 2 x = 12 {/eq}?

## Perpendicular Lines:

(i) To find the slope of a given line, we should convert it to the form {eq}y=mx+b {/eq}. Then {eq}m {/eq} would give the slope.

(ii) Two lines are perpendicular if the product of their slopes is -1. So the slope of one line among them is the negative reciprocal of the other line.

The given equation is:

$$5 y + 2 x = 12 \\ \text{Subtracting 2x from both sides}, \\ 5y=-2x+12 \\ \text{Dividing both sides by 5}, \\ y= \dfrac{-2}{5}x+ \dfrac{12}{5}$$

This is of the form {eq}y=mx+b {/eq}.

Here the slope is, {eq}m= \dfrac{-2}{5} {/eq}.

Two lines are perpendicular if the product of their slopes is -1. So the slope of one line among them is the negative reciprocal of the other line.

So the slope of the line which is perpendicular to the given line is: {eq}\boxed{\mathbf{\dfrac{5}{2}}} {/eq}.

Note: Here {eq}\dfrac{-2}{5} \times \dfrac{5}{2}=-1 {/eq}. So our answer is correct.