1. Geometry: Parallel and Perpendicular Lines
Lesson 5-6
Geometry: Parallel and Perpendicular Lines

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Transparency 6

3. Transparency 6a

4. Objectives Locate points on the coordinate plane
Graph points on a coordinate plane
Write an equation of the line that passes through a given point, parallel to a given line
Write an equation of the line that passes through a given point, perpendicular to a given line

5. Vocabulary Coordinate plane – an x-y grid with axes as reference lines
Quadrant – the axes divide the coordinate plane into 4 regions or quadrants
Graph – is a plot of an ordered pair (x,y) on the coordinate plane
Parallel lines – lines in the same plane that never intersect and have the same slope
Perpendicular lines – lines that meet to form right angles

6. x-y Coordinate Plane Point Plotting Quadrants II I III IV
up 7
left 4
right 5
III IV
down 8
(x, y) (-4, 7) (5, -8)
x – left or right
y – up or down

7. Example 1
Write the slope-intercept form of an equation for the line that passes through (4, –2) and is parallel to the graph of
The line parallel to has the same slope, Replace m with and (x, y) with (4, -2) in the point-slope form.
Point-slope form
Replace m with ½, y with –2, and x with 4.

8. Example 1 cont Simplify. Distributive Property
Subtract 2 from each side.
Write the equation in slope-intercept form.
Answer: The equation is

9. Example 2
Write the slope-intercept form for an equation of a line that passes through (4, –1) and is perpendicular to the graph of
Step 1 Find the slope of the given line.
Original equation
Subtract 7x from each side.
Simplify.
Divide each side by –2.
Simplify.

10. Example 2 cont
Step 2 The slope of the given line is So, the slope of the line perpendicular to this line is the opposite reciprocal of or
Step 3 Use the point-slope form to find the equation.
Point-slope form
and
Simplify.

11. Example 2 cont Simplify. Distributive Property
Subtract 1 from each side.
Simplify.
Answer: The equation of the line is

12. Example 3
Write the slope-intercept form for an equation of a line perpendicular to the graph of and passes through (0, 6).
Step 1 Find the slope of
Original equation
Subtract 5x from each side.
Simplify.
Divide each side by 2.
Simplify.

13. Example 3 cont
Step 2 The slope of the given line is -5/2. So, the slope of the line perpendicular to this line is the opposite reciprocal of -5/2 or 2/5.
Step 3 Substitute the slope and the given point into the point-slope form of a linear equation. Then write the equation in slope-intercept form.
Point-slope form
Replace x1 with 0, y1 with 6, and m with
Distributive Property
Answer: The equation of the line is

14. Summary & Homework Summary: Homework:
Two nonvertical lines are parallel if they have the same slope
Two nonvertical lines are perpendicular if the product of their slopes is -1
Homework:
Pg even
2 graphs