Parallel lines: key idea
Parallel lines have the same slope. So when you are asked for the equation of a line parallel to a given one, start by identifying the slope of the original line and keep that slope unchanged.
Method
- Find the slope of the given line.
- If the line is in slope-intercept form, the slope is the coefficient of (x).
- If it is written in another form, rewrite it if needed so the slope is clear.
- Use the same slope for the new line.
- Use the point given in the problem, if one is provided, and substitute it into a line form such as (y=mx+b) or point-slope form.
- Solve for the missing constant and simplify the equation.
Check your answer
- Confirm that the two lines have the same slope.
- If a point was given, substitute it into your final equation to make sure it works.
- Keep the answer simplified and in the requested form.
Common mistake
Do not copy the intercept from the original line. Parallel lines share slope, not necessarily the same intercept.