Line through (2, 6) with slope 1

Step by step

The question

Question: write the line through (2, 6) 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, 6) to (x, y).

The rise is y − 6: the change in y.

The run is x − 2: the change in x.

Put them in: rise = m × run becomes y − 6 = (x − 2).

This is called point-slope form.

It is made from a point and the slope.

m = 1, and 1 times a bracket is just the bracket.

2 Write as y = mx + b

A bracket with a plus or nothing in front can just be removed.

Now we have y − 6 = x − 2.

We want y by itself.

The − 6 is in the way.

To remove − 6, we add 6.

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

− 6 and + 6 make zero.

Cross them out.

−2 plus 6 is 4.

So y = x + 4.

3 Check

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

We get 6, the y of (2, 6).

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.