# What is the equation of a line that is perpendicular to the line represented by 2x-y = 7?

Mar 23, 2017

You need to define a point through which they both pass.

#### Explanation:

You have $2 x - y = 7$

This becomes $y = 2 x - 7$ and this is of the form of $y = m x + c$ where $m$ is the slope of the line and $c$ is the y-intercept of the line, i.e. where $x = 0$

When 2 lines are perpendicular, the product of their slopes is $- 1$. I can explain this via trigonometry, but that's a higher level of math, which you don't require in this question.

So, let the slope of the required line be $n$

We have $2 \times n = - 1$

$n = - \frac{1}{2}$

In this question, we don't have enough information to calculate the y-intercept, so I'll leave it at

$y = - \frac{x}{2} + d$
where $d$ is the y-intercept of the required line.