today in algebra… review: 5.1-5.3 learning goal: 5.5 writing equations of parallel and...
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TODAY IN ALGEBRA…
REVIEW: 5.1-5.3
Learning Goal: 5.5 Writing equations of Parallel and Perpendicular Lines
STATs: Mid. Ch. 5 Test
Independent Practice
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REVIEW: LINEAR EQUATIONSSLOPE-INTERCEPT FORM:
𝑦=𝑚𝑥+𝑏
𝑠𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
POINT-SLOPE FORM:
𝑦− 𝑦1=𝑚 (𝑥−𝑥1)
𝑠𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛
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REVIEW: Write an equation for the linear function with the values and
𝑓 (𝑥)=𝑥+¿ 6
REMEMBER:
𝑚→𝑏→
(−𝟐 ,𝟏𝟎 ) ,(𝟒 ,−𝟐)
−26
1. Rewrite function values as coordinate pairs (points): 2. Calculate slope:
2. Calculate the y-intercept:
𝑥 𝑦
−2−104−(−2)
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REVIEW: Write an equation of a line that passes through the points in point-slope form, then rewrite the equation in slope-intercept form.
1. Find slope:
2. Choose a point:
3. Plug into Point-Slope form:
¿3
7−(−2)2−(−1)
(2 ,7)
7 23
4. Solve for y to write in Slope-Intercept form:
Slope:Y-intercept:31
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5.5 PARALLEL AND PERPENDICULAR LINESPARALLEL LINES: PERPENDICULAR LINES:
21
4
2
𝑚=12
𝑚=24
¿12
PARALLEL LINES HAVE THE SAME SLOPE
12
𝑚=12
−21𝑚=
−21¿−2
PERPENDICULAR LINES HAVE SLOPES THAT ARE NEGATIVE RECIPROCALS
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5.5 PARALLEL AND PERPENDICULAR LINESExample: Determine the parallel and perpendicular slopes for the following equation
PARALLEL SLOPE:
PERPENDICULAR SLOPE:
Write slope as a fraction𝒎=
−𝟐𝟏
−21 ¿−𝟐
𝟏𝟐
(Same slope)
(flip the fraction and change the sign)
𝒎=−𝟐𝟏
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5.5 PARALLEL AND PERPENDICULAR LINESPRACTICE: Determine the parallel and perpendicular slopes for the following equations
1. 2. 3.
Parallel: Parallel:
Perpendicular: Perpendicular:
Parallel:
Perpendicular:
𝒎=𝟑𝟏
1
Slope for y first!
−𝟏
𝒎=−𝟏𝟏
¿𝟏
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5.5 PARALLEL AND PERPENDICULAR LINESEXAMPLE: Determine which lines, if any, are parallel or perpendicular.
a. b. c. Slope for y first!
Slope for y first!
PARALLEL LINES:line b & line c
PERPENDICULAR LINES:line a & line bline a & line c
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5.5 PARALLEL AND PERPENDICULAR LINESPRACTICE: Determine which lines, if any, are parallel or perpendicular.
a. b. c. Slope for y first!
Slope for y first!
PARALLEL LINES:line a & line b
PERPENDICULAR LINES:line a & line cline b & line c
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−4 −1
REMEMBER:
𝑚→𝑏→
5.5 EQUATIONS OF PARALLEL LINES: Given a point and slope.Write an equation of the line that passes through the point and is parallel to the line .
1. Find slope: 2. Calculate the y-intercept:
SAME SLOPE!!!!!
−4−1
𝑥𝑦
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−3
REMEMBER:
𝑚→𝑏→
5.5 EQNS OF PERPENDICULAR LINES: Given point and slope.Write an equation of the line that passes through the point and is perpendicular to the line .
1. Find slope:
2. Calculate the y-intercept:
NEGATIVE RECIPROCAL!!!!!
−3
𝑥 𝑦
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𝑦=𝑥+¿ 4
REMEMBER:
𝑚→𝑏→
5.5 EQNS OF PERPENDICULAR LINES: Given point and slope.Write an equation of the line that passes through the point and is perpendicular to the line .
1. Find slope:
2. Calculate the y-intercept:
NEGATIVE RECIPROCAL!!!!!
4
𝑥𝑦
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HOW DID YOU “SHAPE” UP??Results for ALL of my Algebra classes:
GRADE NUMBER OF STUDENTS WHO TOOK THE MID CH.5 TEST (40 pts)
1ST PERIOD 6TH PERIOD TOTAL
A/A- 12 4 16
B+/B/B- 5 5 10
C+/C/C- 2 2 4D+/D 0 2 2
F 7 11 18
Average 30.23 26.46 28.35
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HOMEWORK #5:
Pg. 322: 4-10 even, 12, 16, 18-26 even
If finished, work on other assignments:
HW #1: Pg. 286: 3-23 allHW #2: Pg. 286: 24-38 allHW #3: Pg. 296: 3-7, 11-14, 22-25HW #4: Pg. 305: 3-30 all