1. Parallel and Perpendicular Lines

2. Parallel Lines Slope is the same y-intercept is different

3. Perpendicular Lines The y-intercept does not matter The slopes must be opposite inverses of each other –Flip the slope; and –Change the sign.

4. Example 1 Write the equation of a line that goes through the point (5, 2) that is parallel to y = 3x – 5. The only reason we have the equation y = 3x – 5 is to get the slope out of it. The slope is 3. If lines are parallel, they have the same slope—3. Plug the (5, 2) and 3 into y – y 1 = m (x – x 1 ) and simplify. y – 2 = 3(x – 3) y – 2 = 3x – 9 y = 3x - 7

5. Example 2 Write the equation of a line that is parallel to 2x + 3y = 6 that goes through the point (3, 6). Write the equation in slope intercept form. Y = -2/3x + 2. The slope is -2/3. The slope of a line parallel to that is the same. Plug -2/3 and (3, 6) into y – y 1 = m (x – x 1 ) y – 6 = -2/3(x – 3) y – 6 = -2/3x + 2 y = -2/3x + 8

6. Example 3 Write the equation of the line that is perpendicular to y = 3x – 5 that goes through the point (6, 3). The slope of the line above is 3. The slope of the line perpendicular to it is -1/3. Plug that slope and the point (6, 3) into y – y 1 = m (x – x 1 ) and simplify. y – 3 = -1/3(x – 6) y – 3 = -1/3x + 2 y = -1/3x + 5

7. Example 4 Write the equation of a line that is perpendicular to 2x + 3y = 6 that goes through the point (6, 3). Write the equation in slope intercept form. y = -2/3x + 2. The slope is -2/3. The slope of a line perpendicular to that is the 3/2. Plug 3/2 and (6, 3) into y – y 1 = m (x – x 1 ) y – 3 = 3/2(x – 6) y – 3 = 3/2x - 9 y = 3/2x - 6

8. Try these… Write an equation of a line that is: Parallel to y = 4x – 8 going through the point (8, -5) Perpendicular to y = 2x + 3 going through the point (4, –8) Parallel to 2x + 3y = 6, going through the point (6, 8) Perpendicular to 4x – 2y = 8 going through the point (2, 1)

9. Try these-answers Write an equation of a line that is: Parallel to y = 4x – 8 going through the point (8, -5) y = 4x - 37 Perpendicular to y = 2x + 3 going through the point (4, –8) y = -1/2x - 6 Parallel to 2x + 3y = 6, going through the point (6, 8) y = -2/3x + 12 Perpendicular to 4x – 2y = 8 going through the point (2, 1) y = -1/2x + 2