
Parallel Lines LIVE
Presentation
•
Mathematics
•
9th Grade
•
Medium
Christopher Gassler
Used 4+ times
FREE Resource
17 Slides • 8 Questions
1
Parallel Lines
Objective: Identify parallel lines given equations.
2
Multiple Choice
Convert the standard form equation into slope-intercept form.
6x - 7y = -35
y=67x−5
y=76x+5
y=75x−6
y=−76x−5
3
4
Parallel Lines
Lines side by side and having the same distance continuously between them
5
VIDEO
Video illustration of the fact that is stated on the next slide.
6
SLOPE
In the coordinate plane, Parallel Lines have the SAME SLOPE
7
Multiple Choice
REVIEW: What is the slope of the line: y=32x+4
32
−32
23
4
−4
8
SLOPE
In the coordinate plane, Parallel Lines have the SAME SLOPE
Yes its the same slide.
Yes it is here for a reason
Parallel Lines have the SAME SLOPE
9
Multiple Select
Which two lines are parallel?
y=73x−25
y=73x+2
y=37x−25
y=3x+13
y=7x+9
10
11
Multiple Select
Which two lines are parallel?
y=4x−25
y=41x+2
y=x−25
y=4x+13
y=−4x+9
12
What about equations in different forms?
What if one equation is in slope-intercept form.
Like: y = mx + b
And another equation is in point-slope form.
Like: y - y1 = m(x - x1)
13
EXAMPLE 1
Are y = 2x + 4 and y - 19 = 2(x + 21) parallel?
This one is not difficult.
Both forms give us the slope.
14
EXAMPLE 1 (continued)
Are y = 2x + 4 and y - 19 = 2(x + 21) parallel?
Equation 1: y = 2x + 4
The slope is 2
Equation 2: y - 19 = 2(x + 21)
The slope is 2
BOTH have a slope of 2 so YES they are parallel.
15
Multiple Select
Which two lines are parallel?
y=−4x−25
y=41x+2
y+3=4(x−32)
y−2=41(x+67)
y+41=2(x−41)
16
17
But...
What if one equation is in slope-intercept form.
Like: y = mx + b
And another equation is in standard form.
Like: Ax + By = C
Standard Form DOES NOT give us the slope.
We will have to rewrite it to find the slope.
18
VIDEO
Pay attention when he talks about parallel lines.
He mentions perpendicular lines but we will do that in the next lesson.
19
EXAMPLE 2
Are y = 2x + 4 and 2x + 4y = 12 parallel?
IMPORTANT: just because there is a 2 in front of each x DOES NOT mean they are parallel. The second equation needs to be rewritten into slope-intercept form. (y = mx + b)
20
EXAMPLE 2 (cont'd)
Rewrite 2x + 4y = 12 in slope-intercept form.
Overall Goal: get y by itself
Step 1: Subtract the x-term from both sides. (in this case -2x)
Step 2: Divide everything on both sides by the number in front of y
(in this case 4)
21
EXAMPLE 2 (continued)
Are y = 2x + 4 and 2x + 4y = 12 parallel?
Equation 1: y = 2x + 4
Slope = 2
Equation 2: 2x + 4y = 12 rewritten in slope-intercept form: y = -1/2x + 3
Slope = -1/2
Slopes are NOT THE SAME so they are NOT PARALLEL.
22
Multiple Choice
Which line is parallel to the line: 5x+6y=12
y=−65x−2
y=65x+13
y=5x+11
y=−5x−100
23
24
Multiple Choice
Which line is parallel to the line: 3x+4y=−24
y=−43x−1
y=34x+13
y=3x+1
y=−3x−10
y=43x−19
25
Multiple Select
Which lines are parallel to the line: 5x−8y=32
y=85x−1
y=−85x+13
y−12=85(x+13)
y−5=85(x+8)
y−2=−85(x+3)
Parallel Lines
Objective: Identify parallel lines given equations.
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