# How do you write a equation in point -slope form for the line with the given slope and through the given point (-2,-6) and has slope 8/3?

Apr 3, 2015

To see if a point $\left(x , y\right)$ belongs to a line, you need to plug $x$ and $y$ in the equation, and see if creates either a true or false statement.

Now we're watching this problem on the other side: given a point, we want to find the equation of a line which passes through a given point.

Let's recall that, given a point, you have infinite lines passing through that point, one for each possible slope. So, if the slope is also fixed, the solution becomes unique.

The trick is to use the generic equation
$\left(y - {y}_{0}\right) = m \left(x - {x}_{0}\right)$, if ${x}_{0}$ and ${y}_{0}$ are the coordinates of the given point. This line surely passes through $\left({x}_{0} , {y}_{0}\right)$, because these values, if plugged in the equation, gives $0 = 0$, which is of course true.

Then, choosing $m$ as the given slope, gives you the (only) line passing through $\left({x}_{0} , {y}_{0}\right)$ and with slope $m$.

In particular, substituing your values gives the solution $y + 6 = \frac{8}{3} \left(x + 2\right)$