Step by step
The question
Question: write the line through (6, 1) with slope −2/3 in point-slope form.
1 Rise = m × run
We call the slope m.
m = rise over run.
So the rise is m times the run.
Like 8/2 is 4, so 8 is 4 times 2.
Take any point (x, y) on the line.
We go from (6, 1) to (x, y).
The rise is y − 1: the change in y.
The run is x − 6: the change in x.
Put them in: rise = m × run becomes y − 1 = (−2/3) times (x − 6).
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
The −2/3 in front of the bracket multiplies every part inside.
So we write −2/3 times each part.
Work out each multiplication.
Minus times minus is plus.
Now we have y − 1 = −(2/3)x + 4.
We want y by itself.
The − 1 is in the way.
To remove − 1, we add 1.
We do it on both sides, so they stay equal.
− 1 and + 1 make zero.
Cross them out.
4 plus 1 is 5.
So y = −(2/3)x + 5.
3 Check
Let's check: put x = 6 into y = −(2/3)x + 5.
We get 1, the y of (6, 1).
And the number in front of x is −2/3: the slope.
Right!
Let's look back.
First: rise = m × run.
Then: write as y = mx + b.
Last: check.