Question

Which answer is right?

Answer 1

Your answer is the first option.

You use the two points provided to get the slope:
(y2 - y1) / (x2 - x1)
(4 -- 1) / (8 - 2)
(4 + 1) / (6)
(5/6)

Then you work towards the slope-intercept form:
y -- 1 = (5/6) (x-2)
y + 1 = (5/6) (x -2)
y + 1 = (5/6)x - 1 2/3
subtract 1 from each side of the equal sign
y = (5/6)x - (2/3)

Answer 2

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)