Line through (1, 5) parallel to y = 3x + 1 Step by Step

Step by step

The question

Question: find the line through (1, 5), parallel to y = 3x + 1.

y = 3x + 1

new line: through (1, 5)

parallel to this one

1 Slope of the given line

m is the number in front of x: 3.

It is the slope.

b is 1.

m = 3

b = 1

2 Slope of the new line

Parallel lines have the same slope.

So the new line has slope 3 too.

m = 3

Careful!

Same slope, but not the same b.

The new line goes through (1, 5), so it has its own b.

Careful: not y = 3x + 1 ✗

3 Find b

In y = mx + b, put m = 3.

Then use the point (1, 5): put x = 1 and y = 5 in.

5 = 3 × 1 + b

3 times 1 is 3.

5 = 3 + b

We want b by itself.

The 3 is in the way.

To remove 3, we take away 3.

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

5 − 3 = 3 + b ~~− 3~~

3 and − 3 make zero.

Cross them out.

5 minus 3 is 2.

So b = 2.

2 = b

4 Write the equation

Put m = 3 and b = 2 into y = mx + b.

So the new line is y = 3x + 2.

y = 3x + 2

5 Check

Let's check: put x = 1 into y = 3x + 2.

We get 5, the y of (1, 5).

y = 3(1) + 2 = 3 + 2 = 5

And the slope is 3, the same as the given line.

Parallel!

m = 3, the same as the given line

Let's see it on the grid.

The given line in blue.

Our new line y = 3x + 2 in red.

It goes through (1, 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