3.6 Parallel Lines in the Coordinate Plane

What have you learned so far about parallel lines in chapter 3?

What are Parallel Lines• “Lines that never touch in the same plane”• “2 lines that lie in the same plane that will never

intersect”• “Two lines that are coplanar but never meet”• “Two lines that never intersect and are not

touching”• “Never touch, point exactly the same direction”• Always equivalent, meaning they always have

the same measure and will never intersect”

What is slope?How do you find it?

Rise over Run?

What if you just have two points?

(5,3) and (7, 8)

Find the slope of line A and line B.Discuss and check your results with a neighbor.What did you discover?

Lets try this one more

time…

CORRESPONDING ANGLES!!

What’s the formula for a line?(In slope intercept form)

y=mx+bWhat does m stand for?

What does b stand for?

y=mx+b

What are Parallel Lines1. “Lines that never touch in the same plane”2. “2 lines that lie in the same plane that will

never intersect”3. “Two lines that are coplanar but never meet”4. “Two lines that never intersect and are not

touching”5. “Never touch, point exactly the same direction”6. Always equivalent, meaning they always have

the same measure and will never intersect”

Postulate 17Slopes of Parallel Lines

(Pg. 166)• In a coordinate plan, two nonvertical

lines are parallel if and only if they have the same slop. Any two vertical lines are parallel.

1. Coplanar2. Same slope

3.7 Perpendicular Lines in the Coordinate Plane

What have you learned so far about perpendicular lines in chapter 3?

What are Perpendicular Lines?• “2 lines that intersect to make 4 90 degree angles• “2 straight lines that are on the same plane and

intersect at a 90 degree angle”• “Perpendicular lines meet a point where all

angles are 90 degrees”• “Two lines that intersect at one point.”• “Two lines that cross at come point and all 4

angles created are 90 degrees. Line bisects a straight angle.”

y=mx+b

What are Perpendicular Lines?1. “2 lines that intersect to make 4 90 degree

angles2. “2 straight lines that are on the same plane and

intersect at a 90 degree angle”3. “Perpendicular lines meet a point where all

angles are 90 degrees”4. “Two lines that intersect at one point.”5. “Two lines that cross at come point and all 4

angles created are 90 degrees. Line bisects a straight angle.”

Postulate 17Slopes of Perpendicular Lines

(Pg. 166)• In a coordinate plane, two

nonvertical lines are perpendicular if and only if the produce of their slopes is -1.

1. Coplanar2. Slopes are negative reciprocals

Now how well do you know the information?

1. What are two things that have to be true for two lines to be Parallel?

2. What are two things that have to be true for two lines to be perpendicular?

3. What is the slope of a line containing the points (-2,6) and (0,1)?

4. What’s the equation of a line with a slope of 1/3 and a y-intercept of -4?

5. Write an equation of two lines that are parallel.6. Write the equation of two lines that are

perpendicular.