Parallel Lines and Slopes
We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line.
Write the equation of a line that passes through the point and is parallel to the line
Parallel lines have the same slope.
The slope of the line with equation is . So, any line parallel to has the same slope .
Now use the point-slope form to find the equation.
We have to find the equation of the line which has slope and passes through the point . So, replace with , with , and with .
Use the distributive property .
Add to each side.
Therefore, the line is parallel to the line and passes through the point .