Line through (-1, 4) with slope -2

Step by step

The question

Question: write the line through (−1, 4) with slope −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 (−1, 4) to (x, y).

The rise is y − 4: the change in y.

The run is x − (−1): the change in x.

Put them in: rise = m × run becomes y − 4 = −2(x − (−1)).

Taking away a negative is the same as adding.

So it becomes y − 4 = −2(x + 1).

This is called point-slope form.

It is made from a point and the slope.

2 Write as y = mx + b

The −2 in front of the bracket multiplies every part inside.

So we write −2 times each part.

Work out each multiplication.

Now we have y − 4 = −2x − 2.

We want y by itself.

The − 4 is in the way.

To remove − 4, we add 4.

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

− 4 and + 4 make zero.

Cross them out.

−2 plus 4 is 2.

So y = −2x + 2.

3 Check

Let's check: put x = −1 into y = −2x + 2.

We get 4, the y of (−1, 4).

And the number in front of x is −2: the slope.

Right!

Let's look back.

First: rise = m × run.

Then: write as y = mx + b.

Last: check.