Step by step
The question
Question: write the line through (0, 5) 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 (0, 5) to (x, y).
The rise is y − 5: the change in y.
The run is x − 0: the change in x.
Put them in: rise = m × run becomes y − 5 = 3(x − 0).
Taking away 0 changes nothing.
So it becomes y − 5 = 3x.
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
We want y by itself.
The − 5 is in the way.
To remove − 5, we add 5.
We do it on both sides, so they stay equal.
− 5 and + 5 make zero.
Cross them out.
So y = 3x + 5.
3 Check
Let's check: put x = 0 into y = 3x + 5.
We get 5, the y of (0, 5).
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.