Step by step
The question
Question: write the line through (5, 4) with slope 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 (5, 4) to (x, y).
The rise is y − 4: the change in y.
The run is x − 5: the change in x.
Put them in: rise = m × run becomes y − 4 = 3(x − 5).
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
The 3 in front of the bracket multiplies every part inside.
So we write 3 times each part.
Work out each multiplication.
Now we have y − 4 = 3x − 15.
We want y by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
− 4 and + 4 make zero.
Cross them out.
−15 plus 4 is −11.
So y = 3x − 11.
3 Check
Let's check: put x = 5 into y = 3x − 11.
We get 4, the y of (5, 4).
And the number in front of x is 3: the slope.
Right!
Let's look back.
First: rise = m × run.
Then: write as y = mx + b.
Last: check.