Question

Find the Point-Slope equation of the line that passes through the given points. (0,8), (-1,10)

Answer 1

The slope of the equation is -2

Answer 2

So first we need to find the slope. The equation find slope is:

$\frac{ y_{2} -y_{1} }{ x_{2}- x_{1} }$

Either of the points could be denoted as '1' or '2',

Let's plug in the point (0, 8) as '1' and (-1, 10) as '2':

$\frac{10-8}{-1-0} = \frac{2}{-1}=-2$

So we know that the slope, m, is equal to -2.

The point-slope equation is:

$y- y_{1}=m(x- x_{1})$

where m is the slope and $x_{1}$ and $y_{1}$ are the point. So since we have two points here, we can pick one to use for the equation. Let's use (-1, 10):

$y-(10)=-2(x-(-1))$

**We need to make sure that we have accounted for all of the signs. Remember that two negatives equal a positive:

$y-10=-2(x+1)$

And there is your point slope form of the line that passes through the two points.