Solving Equations of Parallel and Perpendicular lines

• The following examples will help you to work through problems involving Parallel and Perpendicular lines.

• Example 1 will show you how to convert a line in Standard Form to a line in Slope Intercept form using Algebraic methods. Then using your result, finding the equation of the line that is perpendicluar to the original given line.

• It is the least efficient method

Example 1Write the equation of a line in slope intercept form that passes

through the point (3,-3), and is perpendicular to the following line: 2x + 4y = 20

• Ax + By = C• 2x + 4y = 20

• Subract 2x from both sides

• 4y = -2x + 20• Divide everything by 4

y = -2/4x + 20/4

• y = -1/2x + 5

•In this example we will convert standard form to slope intercept form. Then we will find the slope of the perpendiular line then use the point slope form and the given point to find the equation we are looking for.

•First off….notice that the question asks for the final answer to be in slope intercept form. y = mx + b

Write the equation of a line in slope intercept form that passes through the point (3,-3), and is perpendicular to the following line:

2x + 4y = 20

• We have just converted the line: 2x +4y = 20 from standard form to slope intercept form:

y = -1/2x +5• And the slope of our original

line is: m=-1/2

We understand that slopes of perpendicuar lines have the relationship of being

• Opposite reciprocals

• So the slope of the line that is perpendicular to our original line must be

m = 2

• Standard Form 2x + 4y = 20

• Converted to Slope Intercept Form:

y = -1/2x +5

• Perpendicular lines have opposite reciprocal slope:

m = 2

• The next step is to find the equation of the line we are looking for.

Example 1Write the equation of a line in slope intercept form that passes

through the point (3,-3), and is perpendicular to the following line: 2x + 4y = 20

We now have the equation of the original line in slope intercept form:

y = -1/2x +5We also know that the slope of

our new (perpendicular) line must

be the opposite reciprocal of our

original line so:

The opposite reciprocal

Of “-1/2” is “2”, thus the slope of

Our new line must be 2

• We now use the Point Slope Form “MOM” and the point that was given to us (3, -3), and substitute our information then simplify.

• y - y1 = m(x - x1)• The y value of our point is -3• y – (-3) = m(x - x1)• The x value of our point is 3• y – (-3) = m(x - 3)• The slope of our perpendicular

line is 2• y – (-3) = 2(x - 3)

Example 1Write the equation of a line in slope intercept form that passes

through the point (3,-3), and is perpendicular to the following line: 2x + 4y = 20

We are now ready to calculate the equation of the line that is perpendicular to our original line that passes through the given point.

To recap: our original line: 2x + 4y = 20

Converted to Slope intercept form:

y = -1/2x +5Finding the slope of the new line:

m = 2Using the given point values: ( 3 , -3 )Substituting the information into the

Point Slope Form y – (-3) = 2(x – 3)

y – (-3) = 2(x – 3)

Distributing: y + 3 = 2x – 6

Simplifying: y = 2x – 6 – 3

Answer: y = 2x – 9 This is the equation of the line that is perpendicular to: 2x + 4y = 20

That passes through the point ( 3, -3)

UR Done!!!

Try the following examples and email me your answer.

nfmath@yahoo.com

• Write the equation of a line in slope intercept form that passes through the point (3,-3), and is perpendicular to the following line:

• 1. 10x + 2y = 30

2. 2x + 3y = 18

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