Step by step
The question
Question: find the line through (−2, 1), parallel to y = 2x − 3.
1 Slope of the given line
m is the number in front of x: 2.
It is the slope.
b is −3.
2 Slope of the new line
Parallel lines have the same slope.
So the new line has slope 2 too.
Careful!
Same slope, but not the same b.
The new line goes through (−2, 1), so it has its own b.
3 Find b
In y = mx + b, put m = 2.
Then use the point (−2, 1): put x = −2 and y = 1 in.
Minus times plus is minus.
2 times −2 is −4.
We want b 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.
1 plus 4 is 5.
So b = 5.
4 Write the equation
Put m = 2 and b = 5 into y = mx + b.
So the new line is y = 2x + 5.
5 Check
Let's check: put x = −2 into y = 2x + 5.
We get 1, the y of (−2, 1).
And the slope is 2, the same as the given line.
Parallel!
Let's see it on the grid.
The given line in blue.
Our new line y = 2x + 5 in red.
It goes through (−2, 1).
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.