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

User DeGo
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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).

User Ventik
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