Line through (2, 5) parallel to y = 2x

Step by step

The question

Question: find the line through (2, 5), parallel to y = 2x − 1.

y = 2x − 1

new line: through (2, 5)

parallel to this one

1 Slope of the given line

m is the number in front of x: 2.

It is the slope.

b is −1.

m = 2

b = −1

2 Slope of the new line

Parallel lines have the same slope.

So the new line has slope 2 too.

m = 2

Careful!

Same slope, but not the same b.

The new line goes through (2, 5), so it has its own b.

Careful: not y = 2x − 1 ✗

3 Find b

In y = mx + b, put m = 2.

Then use the point (2, 5): put x = 2 and y = 5 in.

5 = 2 × 2 + b

2 times 2 is 4.

5 = 4 + b

We want b by itself.

The 4 is in the way.

To remove 4, we take away 4.

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

5 − 4 = 4 + b ~~− 4~~

4 and − 4 make zero.

Cross them out.

5 minus 4 is 1.

So b = 1.

1 = b

4 Write the equation

Put m = 2 and b = 1 into y = mx + b.

So the new line is y = 2x + 1.

y = 2x + 1

5 Check

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

We get 5, the y of (2, 5).

y = 2(2) + 1 = 4 + 1 = 5

And the slope is 2, the same as the given line.

Parallel!

m = 2, the same as the given line

Let's see it on the grid.

The given line in blue.

Our new line y = 2x + 1 in red.

It goes through (2, 5).

They never meet.

Let's look back.

First: slope of the given line.

Then: slope of the new line.

Then: find b.

Then: write the equation.

Last: check.

Answer