Line through (1, 4) parallel to y = -2x + 3 Step by Step

Step by step

The question

Question: find the line through (1, 4), parallel to y = −2x + 3.

y = −2x + 3

new line: through (1, 4)

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 3.

m = −2

b = 3

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 (1, 4), so it has its own b.

Careful: not y = −2x + 3 ✗

3 Find b

In y = mx + b, put m = −2.

Then use the point (1, 4): put x = 1 and y = 4 in.

4 = −2 × 1 + b

Minus times plus is minus.

−2 times 1 is −2.

4 = −2 + b

We want b by itself.

The − 2 is in the way.

To remove − 2, we add 2.

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

4 + 2 = −2 + b ~~+ 2~~

−2 and + 2 make zero.

Cross them out.

4 plus 2 is 6.

So b = 6.

6 = b

4 Write the equation

Put m = −2 and b = 6 into y = mx + b.

So the new line is y = −2x + 6.

y = −2x + 6

5 Check

Let's check: put x = 1 into y = −2x + 6.

We get 4, the y of (1, 4).

y = −2(1) + 6 = −2 + 6 = 4

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 + 6 in red.

It goes through (1, 4).

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