1) If line 1 has a slope of 3, the slope of a perpendicular line 2 needs to be -1/3. 2) If a line has the equation x + 4y = 7, a parallel line will have a slope of -1/4. 3) If a line has the equation x + 4y = 7, a perpendicular line will have a slope of 4.

1. Module 5 Topic 2 Parallel and Perpendicular Slopes

2. Example 1Similar Problem: If line one has a slope of 3, what does the slope of line 2 need to be if the lines are perpendicular?Remember that perpendicular slopes are the opposite reciprocals so if we have 3 then the opposite reciprocal would be -1/3

3. Example 2Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?x + 4y = 7 (solve for y)4y = -x + 7y = -x/4 + 7/4remember that -x/4 the slope is -1/4 so the parallel slope is also -1/4

4. Example 3Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?x + 4y = 7 (solve for y)4y = -x + 7y = -x/4 + 7/4remember that -x/4 the slope is -1/4 so the perpendicular slope is the opposite reciprocal which would be 4/1 or 4

5. Example 4Similar Problem: Write the slope-intercept equation of the line perpendicular to y = 7/2 x - 2, which passes through the point (0, 3).y = 7/2 x - 2 (the slope is 7/2 so the perpendicular slope is -2/7)Use the perpendicular slope and the ordered pair to find b in y = mx + b.y= mx + b0 = -2/7(3) + b0 = -6/7 + b6/7 = bso the equation of the line perpendicular would be y = -2/7x + 6/7

6. Example 5Similar Problem: Write the slope-intercept form of the equation parallel toy= 8x + 3, which passes through (2, -5).y= 8x + 3 (the slope is 3 so the parallel slope is also 3)Use the parallel slope and the ordered pair to find the line of the equation.y= mx + b-5 = 3(2) + b-5 = 6 + b-11 = by= 3x - 11 is the line parallel to the equation y = 3x + 8.

7. Example 6Similar Problem: Write the equation of a line parallel to the line y = 8, that passes through the point (2, 7).Hint: If a line is equal to y and have no x-value then the line parallel is the y-value of the ordered pair.So in this case it is y = 7.

8. Example 7Similar Problem: Write the equation of a line perpendicular to the line y = 8, that passes through the point (2, 7).Hint: If a line is equal to y and have no x-value then the line perpendicular is the is the x-value of the ordered pair.So in this case it is x = 2.