Question

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

Answer 1

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

Explanation:

You have `2x-y=7`

This becomes `y = 2x-7` and this is of the form of `y = mx + 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 `2xxn=-1`

`n = -1/2`

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

`y = -x/2 + d`
where `d` is the y-intercept of the required line.