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

Thinking PageDistance and Midpoint Formula

Draw an example when using distance or midpoint formulas. Write in paragraph form and in

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.

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.

Algebra 1 Review

x

y

x2 x1

y2 y1

P2(x2,y2)

P1(x1,y1)

Slope of a Line: Ratio of its vertical change to the corresponding horizontal change (“rise over run”)

Slope =Rise

Run

y2 y1

x2 x1

Algebra 1 Review

x

y

P2(11,6)

P1(2,3)

Slope of a Line: Ratio of its vertical change to the corresponding horizontal change (“rise over run”)

Slope =Rise

Run

y2 y1

x2 x1

Algebra 1 Review

Find the slope of the line below.

Algebra 1 Review

Graph the line that contains the point (2,1) and the slope of…

m 1

41)

m 22)

m 03)

Forms of a Line

m = slope b = y-intercept

m = slope (x1,y1) = point on line

A,B are integers ≠ 0 and A > 0

Ex : y 1

2x 3

Ex : y 3 1

2(x 0)

Ex : x 2y 6

y mx bSlope-Intercept Form:

y y1 m(x x1)Point-Slope Form:

Ax By CStandard Form:

Graphing Lines in Slope-Intercept Form

Graph the line .

y 3

4x 2

Graphing Lines in Standard Form

Graph the line 2x + 3y = 6.

Method 1: Transform to Slope-Intercept Form

Graphing Lines in Standard Form

Graph the line 2x + 3y = 6.

Method 2: Find intercepts

Using Point-Slope Form

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

Using Point-Slope Form

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

Horizontal and Vertical Lines

y b

Horizontal Lines

Slope = 0Equation:

Vertical Lines

Slope Undefined

x aEquation:

Let’s take a look at the vertical line and horizontal line through the point (-3,1).

Horizontal and Vertical Lines

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

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.

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.

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?

(3.6)/(3.7) Lines in a Coordinate Plane

HOMEWORK:

(3.6)Pgs. 169-170; 2-36 evens (18 problems),

(3.7) Pgs. 177-178; 2-22 evens (11 problems)

Show all work.