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

May 17, 2015

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

$m = \frac{Y 2 - Y 1}{X 2 - X 1}$

so for this question we get.

$m = \frac{- 1 - \left(- 4\right)}{9 - 4}$

$m = \frac{3}{5}$

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

$Y = m X + c$

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:

$- 4 = \left(\frac{3}{5}\right) \left(4\right) + c$
$- 4 = \left(\frac{12}{5}\right) + c$
$- 4 - \left(\frac{12}{5}\right) = c$

$c = - \frac{32}{5}$

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

$Y = \left(\frac{3}{5}\right) X - \left(\frac{32}{5}\right)$