today in algebra… review: 5.1-5.3 learning goal: 5.5 writing equations of parallel and...

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

REVIEW: LINEAR EQUATIONSSLOPE-INTERCEPT FORM:

𝑦=𝑚𝑥+𝑏

𝑠𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

POINT-SLOPE FORM:

𝑦− 𝑦1=𝑚 (𝑥−𝑥1)

𝑠𝑙𝑜𝑝𝑒=𝑟𝑖𝑠𝑒𝑟𝑢𝑛

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)

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

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

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

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

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

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

−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

−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

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

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

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