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Solving Equations of Parallel and Perpendicular lines

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

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Solving Equations of Parallel and Perpendicular lines

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  1. Solving Equations of Parallel and Perpendicular lines • The following examples will help you to work through problems involving Parallel and Perpendicular lines. • Example 4 will show you how to find the slope of a line given only two points and then to find the equation of a line that is parallel to the original. • A follow up example will also show how a perpendicular line can be found.

  2. The Slope Formula m = (y2 – y1)/ (x2 – x1) Given the two points: (4 , 2 ) (-1 , 5) m = (5 – 2)/(-1 – 4) m= 3/-5Thus the slope of our original line is -(3/5). We know that Parallel Lines have the same slope, so the slope of a line Parallel to this one would have a slope of -(3/5) . We also know that the slope of a Perpendicular line is the opposite reciprocal, thus a perpendicular line would have a slope of : 5/3 Example 4Write the equation of two lines in slope interceptform that pass through the point (3,-3), where one line is Parallel and one is Perpendicular to the line passing through these two points (4 , 2 ) (-1 , 5) • In this example we will use the slope formula to find the slope of the original line given only two points. • We will then use the result to find a line that is Parallel , and one that is Perpendicular. • We will then use the point slope formand the given point to find the equations we are looking for. • First off….notice that the question asks for the final answer to be in slope interceptform. y = mx + b

  3. . Now, Since we understand that the slope of a Parallel line is the SAME as the slope of our original line, and that the slope of a perpendicular line is the opposite reciprocal to our original line. Original Slope: -(3/5) Parallel Slope: -(3/5) Perpendicular slope: 5/3 Now we are ready to use the point slope form of a line to calculate the equations of a Parallel line and a Perpendicular line. y - y1 = m(x - x1) Example 4Write the equation of two lines in slope interceptform that pass through the point (3,-3), where one line is Parallel and one is Perpendicular to the line passing through these two points (4 , 2 ) (-1 , 5)

  4. Parallel Line Calculation Using the Point Slope Form “MOM”and the point that was given to us (3, -3), substituting our information and simplifying: y - y1 = m(x - x1) The y value of our point is-3 y – (-3) = m(x - x1) The x value of our point is3 y – (-3) = m(x - 3) The slope of our Parallel line is -(3/5) y – (-3) = -3/5(x - 3) Perpendicular Line Calculation 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 is3 y – (-3) = m(x - 3) The slope of our Perpendicular line is 5/3 y – (-3) = 5/3(x - 3) Example 4Write the equation of two lines in slope interceptform that pass through the point (3,-3), where one line is Parallel and one is Perpendicular to the line passing through these two points (4 , 2 ) (-1 , 5)

  5. Parallel Line Calculation y – (-3) = -3/5(x - 3) Distribute: y – (-3) = -3/5x + 9/5 Simplify : y +3 = -3/5x + 9/5 Common Denominator y +15/5 = -3/5x + 9/5 y = -3/5x + 9/5 -15/5 y= -3/5x -6/5 Answer y= -3/5x -6/5This is the line that is parallel to the line formed by the two given points and passes through the point (3,-3) Perpendicular Line Calculation y – (-3) = 5/3(x - 3) Distribute: y – (-3) = 5/3x -15/3 Simplify : y +3 = 5/3x – 5 y = 5/3x – 5 – 3 y = 5/3x – 8 Answer y= 5/3x – 8This is the line that is perpendicular to the line formed by the two given points and passes through (3, -3) Example 4Write the equation of two lines in slope interceptform that pass through the point (3,-3), where one line is Parallel and one is Perpendicular to the line passing through these two points (4 , 2 ) (-1 , 5)

  6. 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 (2,-2), and is • A. Parallel to • B. Perpendicular to • the line formed by these two points: ( 1, 3) ( 4, 5) • Parallel • Perpendicular There will be more presentations coming so keep checking your email.

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