Step by step
The question
Question: write the line through (−2, −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 (−2, −5) to (x, y).
The rise is y − (−5): the change in y.
The run is x − (−2): the change in x.
Put them in: rise = m × run becomes y − (−5) = 3(x − (−2)).
Taking away a negative is the same as adding.
So it becomes y + 5 = 3(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 in front of the bracket multiplies every part inside.
So we write 3 times each part.
Work out each multiplication.
Now we have y + 5 = 3x + 6.
We want y by itself.
The + 5 is in the way.
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
+ 5 and − 5 make zero.
Cross them out.
6 minus 5 is 1.
So y = 3x + 1.
3 Check
Let's check: put x = −2 into y = 3x + 1.
We get −5, the y of (−2, −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.