Line through (2, 2) with slope -1

Step by step

The question

Question: write the line through (2, 2) with slope −1 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, 2) to (x, y).

The rise is y − 2: the change in y.

The run is x − 2: the change in x.

Put them in: rise = m × run becomes y − 2 = −(x − 2).

This is called point-slope form.

It is made from a point and the slope.

2 Write as y = mx + b

A minus in front of a bracket changes the sign of every part inside.

x becomes −x.

−2 becomes 2.

Now we have y − 2 = −x + 2.

We want y by itself.

The − 2 is in the way.

To remove − 2, we add 2.

We do it on both sides, so they stay equal.

− 2 and + 2 make zero.

Cross them out.

2 plus 2 is 4.

So y = −x + 4.

3 Check

Let's check: put x = 2 into y = −x + 4.

We get 2, the y of (2, 2).

And the number in front of x is −1: the slope.

Right!

Let's look back.

First: rise = m × run.

Then: write as y = mx + b.

Last: check.