Step by step
The question
Question: write the line through (2, −3) with slope −3/2 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 (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) = (−3/2) times (x − 2).
Taking away a negative is the same as adding.
So it becomes y + 3 = (−3/2) times (x − 2).
This is called point-slope form.
It is made from a point and the slope.
2 Write as y = mx + b
The −3/2 in front of the bracket multiplies every part inside.
So we write −3/2 times each part.
Work out each multiplication.
Minus times minus is plus.
Now we have y + 3 = −(3/2)x + 3.
We want y by itself.
The + 3 is in the way.
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
3 minus 3 is 0.
So y = −(3/2)x.
3 Check
Let's check: put x = 2 into y = −(3/2)x.
We get −3, the y of (2, −3).
And the number in front of x is −3/2: the slope.
Right!
Let's look back.
First: rise = m × run.
Then: write as y = mx + b.
Last: check.