Point Slope Form

    \[y-y_1=m(x-x_1)\]

All that is needed is 2 points, or 1 point and a slope. Either way the slope is going to be discovered. y_1, and x_1 are from the point (x_1,y_1).

 

1 Point and slope

If I need a line to pass through the point (3,5) and has slope of 4, then I just need to plug my pieces into the form.

x_1=3
y_1=5
m=4

so my equation looks like…

    \[y-5=4(x-3)\]

That’s it!

 

 

With 2 Points

The process is exactly the same with 2 points, except that the slope needs to be calculated.

Step 1: Calculate the slope \frac{y_1-y_2}{x_1-x_2}

Step 2: Pick which point you like better.

Step 3: Use slope from step 1, your favorite point, then plug  in to point-slope form.

Find the equation of the line passing through the points (1,1), and (-3,5)

Step 1: \frac{1- -3}{1-5}=\frac{2}{-4}=-\frac{1}{2}

Step 2: I think (1,1) is a fine looking point, so I’m going to use it!

Step 3: (y-1)=-\frac{1}{2}(x-1)