Question

How do you write the point slope form of the equation given (4,-5) and m=6?

Answer 1

`y=6x-29`
graph{y=6x-29 [-10, 10, -5, 5]}

Explanation:

The formula to find the equation is `y=mx+b`

Since we know that `m=6`, the equation we have so far would be `y=6x+b`.

Now, we will find `b`.

Plug in `(4, -5)` where `x=4` and `y=-5`

`-5=6*4+b`

Switch sides:
`6*4+b=-5`

Multiply the numbers:
`24+b=-5`

Subtract `24` from both sides:
`24+bcolor(red)-color(red)24=-5color(red)-color(red)24`

Simplify:
`b=-29`

Therefore, the whole equation is:
`y=6x-29`.

Answer 2

`y+5=6(x-4)`

Explanation:

Remember that the point-slope form equation looks like this:

`y-k=m(x-h)`

Where `h` and `k` represents a point on the line and `m` is the slope.

The point should have the coordinates like this: `(h,k)`

What we have to do is substitute the values in like so:

`y-k=m(x-h)`
`y-(-5)=6(x-4)`
So the answer must be:
`y+5=6(x-4)`

Sweeeeet