# High School Math : How to find the equation of a parallel line

## Example Questions

### Example Question #61 : Algebra I

What line is parallel to through the point ?      Explanation:

The given line can be rewritten as , which has slope .

If the new line is parallel to the old line, it must have the same slope.  So we use the point-slope form of an equation to calculate the new intercept. becomes where .

So the equation of the parallel line is .

### Example Question #1 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to      Explanation:

Since parallel lines share the same slope, the only answer that works is ### Example Question #3 : How To Find The Equation Of A Parallel Line

Given the equation and the point , find a line through the point that is parallel to the given line.      Explanation:

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula, ,

where represents the slope and and represent the given points, plug in the points given and simplify into standard form:   ### Example Question #4 : How To Find The Equation Of A Parallel Line

What line is parallel to through ?      Explanation:

Parallel lines have the same slopes.  The slope for the given equation is .  We can use the slope and the new point in the slope intercept equation to solve for the intercept:   Therefore the new equation becomes: ### Example Question #5 : How To Find The Equation Of A Parallel Line

What line is parallel to through ?      Explanation:

Parallel lines have the same slope.  The slope of the given line is .

Find the line with slope through the point by plugging this informatuon into the slope intercept equation, : , which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes , and converting to standard form gives .

### Example Question #1 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to the line that goes through points and .     Parallel lines share the same slope. Because the slope of the original line is , the correct answer must have that slope, so the correct answer is  