First find the slope, m, for the line y=mx+b.
m=(y2-y1)/(x2-x1)
m=(4--1)/(8-2)
m=5/6
The point slope form of a line is:
y-y1=m(x-x1) where m is the slope and (x1,y1) is any point on the line. We know that m=5/6 and if we use the point (2, -1) you get:
y+1=(5/6)(x-2)
Now the standard form of the line is ax+by=c, so we can rearrange the above into that form, multiply both sides by 6
6y+6=5(x-2)
6y+6=5x-10 subtract 5x from both sides
-5x+6y+6=-10 subtract 6 from both sides
-5x+6y=-16
So the answer is:
y+1=(5/6)(x-2); -5x+6y=-16
I would just note that by convention the standard form should be expressed with a positive coefficient for x, which means that technically you would divide the equation that we found by -1 to get:
5x-6y=16
Even though your choices do not reflect this, this is the correct form by convention....(although they are of course equivalent in every way)
