Step by step
The question
Question: write the line through (4, 0) with slope 1/2 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, 0) to (x, y).
The rise is y − 0: the change in y.
The run is x − 4: the change in x.
Put them in: rise = m × run becomes y − 0 = (1/2) times (x − 4).
Taking away 0 changes nothing.
So it becomes y = (1/2) times (x − 4).
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
The 1/2 in front of the bracket multiplies every part inside.
So we write 1/2 times each part.
Work out each multiplication.
So y = (1/2)x − 2.
y is already by itself.
3 Check
Let's check: put x = 4 into y = (1/2)x − 2.
We get 0, the y of (4, 0).
And the number in front of x is 1/2: the slope.
Right!
Let's look back.
First: rise = m × run.
Then: write as y = mx + b.
Last: check.