To write the equation of line in y = mx + b form, we need
to identify the slope of the line and the y-intercept.
I would start by setting up a coordinate
system and plotting both points.
I have shown this below.
Let's start with our first point, (3, -1) which we call point A.
Now our second point, (6, 1) which we call point B.
To get from point A to point B, we rise 2 units and run 3 units.
So we know that our slope is 2/3.
However, we need the y-intercept.
Remember, this is the point where the line crosses the y-axis.
Since point B is farther from y-axis,
we need to go in the other direction.
So starting at point A, we go down 2 and to the left 3.
Remember, -2/-3 is 2/3 since a negative/negative = positive.
Now plot point C.
Notice that point C is on the y-axis.
It has the coordinates (0,-3).
Now we know our slope and y-intercept.
So our equation reads 2/3x - 3.
The slope is positive since the line is going up.