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