Question

How can you find the equation of a line that is parallel/perpendicular to a given line

Answer 1

In the Slope-Intercept Form, m is the slope and b is the y-intercept.

Finding The Equation of a Line Parallel to the Given Line: Let the given line be line a and the parallel line be line b.

1) Find the slope of line a.

Example: Line a -->
`y = 5x + 2`. The slope is 5.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of a point located on line b.

Example: The slope is 5 and the point is (2, 3), use the Slope-Intercept Formula,
`y=mx+b` --->
`3 = 5(2) + b`. Then you solve for b.

`3 = 5(2) + b`

`3 = 10 + b`

`3 - 10 = 10 - 10 + b`

`-7 = b`
`b=-7`

The y-intercept of line b is -7

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is 5 and the y-intercept is -7. The equation of line b is
`y = 5x - 7`.

Finding The Equation of a Line Perpendicular to The Given Line: Let the given line be line a and the perpendicular line be line b.

1) Find the opposite reciprocal of the slope of line a.

Example: Line a -->
`y=5x+2`. The slope is 5, to find the opposite reciprocal of the slope you use n -->
`-(1)/(n)`. In this case, it would be
`-(1)/(5)`. The opposite reciprocal of the slope of line a is
`-(1)/(5)`, which would be the slope of line b.

2) Find the y-intercept of line b.

To do this, you need to be given the coordinates of the point where line a and line b both intersect.

Example: The slope of line b is
`-(1)/(5)` and the point is (1, 7), use the Slope-Intercept Formula,
`y=mx+b` --->
`7=-(1)/(5)(1) + b`. Then you solve for b.

`7=-(1)/(5)(1) + b`

`7=-(1)/(5) + b`

`7+(1)/(5)=-(1)/(5) + (1)/(5) + b`

`7(1)/(5) =b`
`b=7(1)/(5)`

The y-intercept of line b is
`7(1)/(5)`.

3) Finally, plugin the slope and the y-intercept into the Slope-Intercept Form.

Example: The slope of line b is
`-(1)/(5)` and the y-intercept is
`7(1)/(5)`. The equation of line b is
`y=-(1)/(5)x+7(1)/(5)`.