1. Solving Equations of Parallel and Perpendicular lines The following examples will help you to work through problems involving Parallel and Perpendicular lines. Example 3 will show you how to use the relationships between the Coefficients of the terms of a line written in Standard Form to the slope of a line. Then, using your result, finding the equation of the line that is Parallel to the original given line. It is a very efficient method

2. Example 3 W rite the equation of a line in slope intercept form that passes through the point (3,-3), and is Parallel to the following line: 2x + 4y = 20 Ax + By = C 2x + 4y = 20 The Coeffiecients of the line are A = 2, B = 4, and C = 20 If we convert the equation from Standard Form to Slope Intercept Form We get the following: Ax + By = C Move the Ax term to the other side by subtracting Ax: By = -Ax + C Divide everything by B y = (-A/B)x + C/B In this example we will use the coefficients of the terms of the line written in Standard Form to quickly find the slope of the line that is Parallel to the original line. We will 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

3. Write the equation of a line in slope intercept form that passes through the point (3,-3), and is Parallel to the following line: 2x + 4y = 20 We have just established the relationships between the Coefficients of a line written in Standard Form with the Slope and Y intercept of a line written in Slope Intercept form. We are only interested in the Slope relationship at this time. Now, Since we understand that the slope of a Parallel line is the SAME as the slope of our original line, we can see that the Slope of our new line will be (-A/B) Standard Form: Ax + By = C Slope; “Original Line “ m = (-A/B) Y intercept: b = C/B -------------------------------------- m = (-A/B) This is the slope of the line that is Parallel to the slope of the original line. Note: Parallel Lines have the SAME slope.

4. Example 3 W rite the equation of a line in slope intercept form that passes through the point (3,-3), and is Parallel to the following line: 2x + 4y = 20 We now have the slope of the Parallel line simply by understanding the relationship of the coefficients. 2x + 4y = 20 Parallel slope is: m = -A/B Which is: m = -2/4, thus m = -1/2 Now we have the Slope of the line we are looking for, and we have been given one point on the new line, (3,-3), so we can use the P oint Slope Form to find the equation of the new parallel line. 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 Parallel line is -1/2 y – (-3) = -1/2(x - 3)

5. Example 3 W rite the equation of a line in slope intercept form that passes through the point (3,-3), and is Parallel to the following line: 2x + 4y = 20 RECAP!! Write the original equation: Determine the slope of the Parallel line using coefficients: (parallel slope) m= -A/B Use the slope and the point given and substitute into the point slope form: Simplify: Combining like terms, we need a common denominator, thus we convert -3 into -6/2 and combine with 3/2 2x + 4y = 20 m = -1/2 Given point ( 3, -3) Point slope Form: y – y1 = m(x – x1) Substituting: y – (-3) = -1/2(x – 3) Distributing: y + 3 = -1/2x + 3/2 Simplifying: y = -1/2x + 3/2 – 3 y = -1/2x + 3/2 – 6/2 Answer: y = -1/2x – 3/2 This is the equation of the line that is Parallel to: 2x + 4y = 20,that passes through the point ( 3, -3) UR Done!!!

6. Try the following examples and email me your answer. nfmath@yahoo.com nfmath@yahoo.com Write the equation of a line in slope intercept form that passes through the point (4,-2), and is Parallel to the following line: 1. 6x - 2y = 24 2. 2x + 7y = 28 There will be more presentations coming so keep checking your email.