1. Lesson 5: (3.6)/(3.7) Parallel and Perpendicular Lines

2. Thinking Page Distance and Midpoint Formula Draw an example when using distance or midpoint formulas.
Write in paragraph form and in

3. What are we learning? Students will… graph lines given their equations
write equations of lines
relate slope and parallel lines
relate slope and perpendicular lines
Evidence Outcome: Students will express properties with equations (coordinate geometry). (HS 4.3a)
Purpose: In the unit, we have continued to show the relationships of lines, segments, rays, planes, etc… Now going to show the relationship of slope to parallel lines and perpendicular lines. In life, architects use parallel and perpendicular lines to enhance the beauty of a home.

4. This home is in New Zealand and is a great example of modernist architecture, the straight lines dominate the design, in both indoors and outdoors, and in the decoration and furniture. Tones, black, white and beige create pleasant atmospheres and minimalism is the rule of thumb. Parallel and perpendicular lines to a wall defined exterior with different heights, the lines create a dramatic, but subtle elegance to the home, textures and colors that overlap and mix, fitting together like a puzzle.

5. Algebra 1 Review
Slope of a Line: Ratio of its vertical change to the corresponding horizontal change (“rise over run”) x y

6. Algebra 1 Review
Slope of a Line: Ratio of its vertical change to the corresponding horizontal change (“rise over run”) x y

7. Algebra 1 Review
Find the slope of the line below.

8. Algebra 1 Review
Graph the line that contains the point (2,1) and the slope of… 1) 2) 3)

9. Forms of a Line Slope-Intercept Form: m = slope b = y-intercept
Standard Form:
A,B are integers ≠ 0 and A > 0
Point-Slope Form:
m = slope (x1,y1) = point on line

10. Graphing Lines in Slope-Intercept Form
Graph the line

11. Graphing Lines in Standard Form
Graph the line 2x + 3y = 6.
Method 1: Transform to Slope-Intercept Form

12. Graphing Lines in Standard Form
Graph the line 2x + 3y = 6.
Method 2: Find intercepts

13. Using Point-Slope Form
Write an equation in point-slope form of the line through point P(-1,4) with slope 3.

14. Using Point-Slope Form
Write an equation in point-slope form of the line through the points A(-2,3) and B(1,-1).

15. Horizontal and Vertical Lines
Let’s take a look at the vertical line and horizontal line through the point (-3,1).
Horizontal Lines
Slope = 0
Equation:
Vertical Lines
Slope Undefined
Equation:

16. Horizontal and Vertical Lines
Write equations for the horizontal line and the vertical line that contain the point (2,-5).

17. Slope and Parallel Lines
Slopes of Parallel Lines:
1) If two nonvertical lines are parallel, their slopes are equal.
2) If the slopes of two distinct nonvertical lines are equal, the lines are parallel.
3) Any two vertical lines are parallel.

18. Slope and Perpendicular Lines
Slopes of Perpendicular Lines:
1) If two nonvertical lines are perpendicular, the product of their slopes is -1.
2) If the slopes of two lines have a product of -1, the lines are perpendicular.
3) Any horizontal line and vertical line are perpendicular.

19. Thinking Page
Directions: Write in paragraph form and in complete sentences. Answer the following questions. What was the teaching point of the lesson? How is it meaningful to you and relevant beyond the lesson?

20. (3.6)/(3.7) Lines in a Coordinate Plane
HOMEWORK: (3.6)Pgs ; 2-36 evens (18 problems), (3.7) Pgs ; 2-22 evens (11 problems) Show all work.