1. Slopes of Parallel and Perpendicular Lines (3.6) Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and perpendicular lines

3. Slopes of Parallel Lines  Slopes of parallel lines are equal =  Any 2 vertical lines are parallel; any 2 horizontal lines are parallel  Test whether 2 non-vertical or non- horizontal lines are // by comparing slopes EXAMPLE #1: Line 1 contains points A(1,5) and B(3,1) Line 2 contains points C(3,3) and D(1,-4) Are the 2 lines parallel? Explain.

4. Are the two lines parallel ? Example #2  Line 1 contains P(0,3) and Q(-2,5)  Line 2 contains R(0,-7) and S(3,-10)

5. Are the lines parallel ? Example #3  Are the lines and parallel? Explain. Compare the SLOPES by re-writing in slope-intercept form.

6. How do you write the equation of a line?  There are 3 forms used to write the equation of a line…

7. Writing the Equations of Parallel Lines Example #4 Write an equation of a line parallel to that contains the point (1,-2). Identify slope. Use this slope and given point to write equation:

8. Example #5  Write the equation for the line that is parallel to y=3x+5 that contains the point (-3,7).

9. Slope and Perpendicular Lines  Perpendicular Lines have slopes that are opposite, reciprocals of each other.  Their slopes’ product is -1.  Any vertical and any horizontal line are perpendicular. Slope:Perpendicular Slope:

10. Are the 2 lines perpendicular ? To answer this question, do the following: 1. Find their slopes. 2. If their slopes are opposite, reciprocal, then they are perpendicular. Example #1: Line 1: (-2,3) and (6,-3) Line 2: (-3,-2) and (0,2)

11. Are the 2 lines perpendicular ? 2. 3. 4.

12. Writing the Equation of Perpendicular Lines Step 1. Identify the slope of the given line. Step 2. Find the slope of the line perpendicular to the given line (opposite, reciprocal) Step 3. Use the slope from Step 2 and given point to write new equation.

13. Writing the equation of perpendicular lines Example #5 Write the equation of the line that is perpendicular to and passes through the point (1,-2)

14. Example #6 Write the equation for the line that is perpendicular to y=3x+5 that contains the point (-3,7).