Question

What is the equation in point-slope form of the line given (4, –4) and (9, –1)?

Answer 1

Firstly in this question we would need to find the "slope" or otherwise known as the gradient. we use the formula.

`m= (Y2 - Y1)/(X2-X1)`

so for this question we get.

`m = (-1 - ( -4))/(9-4)`

`m = 3/5`

now we take a look at our equation for a straight line, which is.

`Y = mX + c`

we have now got a value for `m` and we need to solve for a value for `c`.

to do this, we use the `X` and `Y` from either of the given points and put them into our formula. so we have:

`-4 = (3/5)(4) + c`
`-4 = (12/5) + c`
`-4 - (12/5) =c`

`c = -32/5`

now all we need to do is insert our value for `c` into our straight line equation. thus we end up with.

`Y = (3/5)X - (32/5)`