Step by step
The question
Question: write the line through (4, 1) with slope 2 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 (4, 1) to (x, y).
The rise is y − 1: the change in y.
The run is x − 4: the change in x.
Put them in: rise = m × run becomes y − 1 = 2(x − 4).
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Work out each multiplication.
Now we have y − 1 = 2x − 8.
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.
−8 plus 1 is −7.
So y = 2x − 7.
3 Check
Let's check: put x = 4 into y = 2x − 7.
We get 1, the y of (4, 1).
And the number in front of x is 2: the slope.
Right!
Let's look back.
First: rise = m × run.
Then: write as y = mx + b.
Last: check.