Question

What is the equation of the line which is parallel to `y = 2x-9` and which passes through the point `(4,2)`?

Answer 1

`y=2x-6`

Explanation:

The original formula for the slope is given in the form of

`y=mx+b`,

where `m` is the slope and `b` is the place where the line intersects the y axis, or "`y`-intercept".

In a parallel line, the slope is the same, but the `y`-intercept is different. So, your `m` value remains the same, `(m=2)` but you pick a different `b` value.

In order to choose the appropriate `b` value for the equation of the line we want, we will need to find a line with the same slope that passes through the point `(4,2)` which is `(x,y)`

So, with `m=2`, set `y=2` and `x=4`, and notice that we get `2=2(4)+b`.

Then we have `2=8+b`, which means the choice of `b` we want is `b=-6`.

This gives us the parallel line `y=2x-6`.