Line through (1, 1) with slope 5

Step by step

The question

Question: write the line through (1, 1) with slope 5 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 (1, 1) to (x, y).

The rise is y − 1: the change in y.

The run is x − 1: the change in x.

Put them in: rise = m × run becomes y − 1 = 5(x − 1).

This is called point-slope form.

It is made from a point and the slope.

2 Write as y = mx + b

The 5 in front of the bracket multiplies every part inside.

So we write 5 times each part.

Work out each multiplication.

Now we have y − 1 = 5x − 5.

We want y by itself.

The − 1 is in the way.

To remove − 1, we add 1.

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

− 1 and + 1 make zero.

Cross them out.

−5 plus 1 is −4.

So y = 5x − 4.

3 Check

Let's check: put x = 1 into y = 5x − 4.

We get 1, the y of (1, 1).

And the number in front of x is 5: the slope.

Right!

Let's look back.

First: rise = m × run.

Then: write as y = mx + b.

Last: check.