Question

What is the equation of the line perpendicular to `y=-3/7x` that passes through `(5,7)`?

Answer 1

`y=3/7x+34/7`

Explanation:

So, the line we need to determine is `"perpendicular"` to the given line. Thus, the slope is the `"negative reciprocal"` of the slope of the line given.

Since the line given is in `"slope-intercept form"`, we can easily find the slope as it will be the constant being multiplied to the `x` term. In this line, it will be `-3/7`.

Then, we calculate the `"negative reciprocal"` of it. First negating it, we get `3/7`. Then, taking the reciprocal, it will be `7/3`.

Now, we have our slope of our new line. We are also given a point, so we can use `"point-slope formula"` to determine our new line.

Doing so yields:

`(y-7)=3/7(x-5)`

Now, this is an acceptable form of a line. But since the question gives you a line in `"slope-intercept"` form, you should give your answer in that form as well.

Converting this line to slope intercept, we get:

`y-7=3/7x-15/7`

`y=3/7x-15/7+49/7`

`y=3/7x+34/7`