Jigsaw Activity

Linear Equation

Name: _____________________________________

Period: _______ Partner’s names: _________________________

Ms. Nhotsoubanh

Directions:

You will have 2 days to work on the Jigsaw Activity on Linear Equations.

You will work with your shoulder partner and another pair (that equals 4 students per group). Whatever is not completed in class must be completed over the winter break.

This lesson requires you to read and have a conversation with your group.

slope  

y-­‐intercep

t  

x input

y output

4 12

6 17

8 22

10 27

_____________________________

_____________________________

Expert Sheet 1

“Transposing a Linear Equation into Slope-Intercept form”

Aim: Students will be able to transpose linear equations into slope-intercept form. Standards: A.A.34 & A.A.35

Example 1. Transpose the equation into slope-intercept form. 2x + y = -8 -2x -2x y = -2x – 8 Slope-intercept form: y = -2x – 8

m = !2

1 b = -8

m represents the slope b represents the y-intercept

Example 2. Transform the equation into slope-intercept form. y = mx + b 12 + 3y = 9x -12 -12 3y = 9x – 12 3 3 3 y = 3x – 4 Slope-intercept form: y = 3x – 4

m = 3

1 b = -4

m represents the slope b represents the y-intercept

Directions: Transpose the equation into standard form. 3. 6 + y = 3x m = _______ b = ________

4. 3y = 4x – 9 m = _______ b = ________

5. y + 2x = 10 m = _______ b = ________

6. x – y = 4 m = _______ b = ________

7. 3x – 9y = 18

m = _______ b = ________

8. x = 5y

m = _______ b = ________

y = mx + b Steps: 1. Subtract 2x from both sides. Can’t combine -8 & -2x *You want the “y” to be by itself.

Steps: 1. Subtract 12 from both sides. Can’t combine 9x & -12 2. Divide 3 to both sides. * You want the “y” to be by itself.

slope

y-in

terc

ept A point on a line

that crosses the y-axis

Expert Sheet 2 “Write an Equation of a Line”

Aim: Write the equation of a line, given its slope and the coordinates of a point on the line Standards: A.A.34 & A.A.35

Ex1. Write an equation of a line that has a

slope of 52

and y intercept of −3.

y = mx + b

Equation: y =52

x – 3

Steps to writing an Equation of a Line

Case 1. Given a Slope & a y-intercept Substitute the slope (m) and y-intercept (b) into the equation y = mx + b. See example 1 and 2

Ex2. Write an equation of a line that has a slope of 1 and y intercept of 0.

y = mx + b (y-intercept is 0 so there is no “b”)

Equation: y = 1x or y = x

Ex3. Write an equation of a line that has a slope of −4 and x-intercept 3. y = mx + b m = -4 b = ? 0 = -4(3) + b 0 = -12 + b +12 +12 12 = b so m = -4 and b = 12 therefore the equation is Equation: y = -4x + 12

Steps to writing an Equation of a Line Case 2. Given Slope & x-intercept 1. Substitute the slope (m) in the equation: y = mx + b. 2. To find b, substitute the x-intercept coordinates (x, 0) in the equation y = mx +b. See example 3

4. Write an equation of a line that has a

slope of 23

and y intercept of 4.

Equation: _____________________________

5. Write an equation of a line that has a slope of zero and a y-intercept of 8. Equation: _____________________________

6. Write an equation of a line that has a slope of -1 and a x-intercept of 3. Equation: _____________________________

7. Write an equation of a line that has a slope of 6 and a x-intercept of 0. Equation: _____________________________

Since the x-intercept is 3, the coordinate is (3, 0). Substitute 3 in for x and 0 in for y in the equation y = mx + b

ê ê

ê

Expert Sheet 3 “Write an Equation of a Line, Given 2 Points”

Aim: Write the equation of a line, given the coordinates of two points on the line Standards: A.A.34 & A.A.35

Example. Write an equation of a line that passes through points (−2, 5) and (4, 8).

m = y1! y

2

x1! x

2

m = 5 ! 8

!2! 4=!3

!6=1

2

since m = 1

2 now follow step 2.

Need to find the y-intercept (b). y = mx + b using point (4, 8)

8 = 1

2(4) + b

8 = 2 + b -2 -2 6 = b

Equation: y = 1

2x + 6

Steps to writing an Equation of a Line

Case 3. (Given 2 points) 1. Use the slope formula to find the slope of the 2 given points. Substitute in for the x’s and the y’s. Point 1 (!!,!!)

Point 2 (!!,!!)

Slope formula (m) = y1! y

2

x1! x

2 12

12

xxyy

−

−or

2. Pick one of the points, then substitute the point and the slope into the equation y = mx + b

Directions: Find the equation of a line that passes through the given points. 1.) (-3, -4) and (2, 11)

2.) (-6, -5) and (6, -13)

3.) (0, 2) and (6, 2)

4.) (-10, 7) and (-10, -4)

(x, y) (-2, 5) (4, 8)

(x1, y1) (x2, y2)

*you can pick any of the 2 points

Expert Sheet 4 “Write an Equation of a Line, Given a Graph”

Aim: Write the equation of a line, given a graph. Standards: A.A.34 & A.A.35

How to find the slope: Pick 2 points on the line. Look at Line P. Count the # of units going up to the other point then count the # of units going to the right of the other point. How to find the y-intercept: It is the point that crosses the y-axis.

Example 1. Write the equation of line P in the graph.

Slope (m) = 2

1

y-intercept (b) = -1 Equation: y = 2x – 1

Example 2: Write the equation of line K in the graph. Slope (m) = 0 y-intercept (b) = 3 y = 0x + 3 or y = 3 Equation: y = 3

Write the equation of lines in the graph. 3. Line A: ________________________ slope(m) = ________ y-intercept(b) = ______ 4. Line B: ________________________ slope(m) = ________ y-intercept(b) = ______ 5. Line C: ________________________ slope(m) = ________ y-intercept(b) = ______ 6. Line D: ________________________ slope(m) = ________ y-intercept(b) = ______

y

x -6 -4 -2 2 4 6

6 4 2

-2 -4 -6

Line P

Line K

Steps: 1. Find the slope of the line. 2. Find the y-intercept of the line. 3. Substitute the slope and y-intercept into the equation y = mx + b

• •

y

x -6 -4 -2 2 4 6

6 4 2

-2 -4 -6

Line A

Lin

e B

Line C

Line D

2

1

rise

run

Expert Sheet 5

“Write an Equation of a Line, Given a Table” Aim: Write the equation of a line, given a table. Standards: A.A.34 & A.A.35

Example 1 (x, y) y = mx + b Point (0, -6) -6 = 2(0) + b -6 = 0 + b -6 = b

Function (equation): y = 2x – 6 Check by typing the equation y = 2x – 6 into your graphing calculator. Go to the table and check the points.

x y

0 -6

1 -4

2 -2

3 0

4 2

Steps: 1. Find the pattern of the values in the x and y columns in the table. The pattern is your slope, which is represented by “m”.

Slope (m) = change in y - valueschange in x - valus

=!y!x

=2

1 2. Pick any point from the table and substitute the input(x) and the output(y) into the linear equation: y = mx + b 3. Solve the equation to get the value of “b” which is the y-intercept (where it crosses the y-axis). 4. To get the linear equation: find the slope (m) and the y-intercept (b) and substitute them into the equation y = mx + b.

Example 2 (x, y) y = mx + b Point (-3, 6)

6 = 32−

(-3) + b

6 = 2 + b -2 -2 4 = b

Function (equation): y = 32

− x + 4

x y

-3 6

0 4

3 2

6 0

9 -2

Now it’s your turn: 3. Function (equation): ______________________

x y

-2 16

2 0

6 -16

10 -32

14 -48

4. Function (equation): ______________________

x y

0 1

6 -9

12 -19

18 -29

24 -39

5. Function (equation): ______________________

x y

8 37

13 62

18 87

23 112

28 137

+2

+2

+2

+2

+1

+1

+1

+1

-2

-2

-2

-2

+3

+3

+3

+3

! =∆!∆! =

−23

Substitute (x, y) into the equation y = mx + b

! =∆!∆! =

21

Got Slope? Plot the points on each graph and answer the questions below.

Graph 1 A(-3,-2) and B(1, 2)

Graph 2 C(-2,3) and D(2, -1)

Graph 3 E(-2, 3) and F(3, 3)

Graph 4

G(2, 3) and H(2, -3)

What do you notice about the slope of the line? __________________________ __________________________ __________________________

What do you notice about the slope of the line? __________________________ __________________________ __________________________

What do you notice about the slope of the line? __________________________ __________________________ __________________________

What do you notice about the slope of the line? __________________________ __________________________ __________________________

Example Find slope of line H.

Your Turn Directions: • Find the numeric slope (written as a fraction) of each line • Then name the type of slope (positive, negative, no slope, or zero slope) for each line. Graph 1

Slope = __________ Type: ___________________

Graph 2

Slope = __________ Type: __________________

Graph 3

Slope = __________ Type: ___________________

Graph 4

Slope = __________ Type: ___________________

y

x

1 2 3 -3 -2 -1 -1 -2 -3

3 2 1

y

x

1 2 3 -3 -2 -1 -1 -2 -3

3 2 1

y

x

1 2 3 -3 -2 -1 -1 -2 -3

3 2 1

y

x

1 2 3 -3 -2 -1 -1 -2 -3

3 2 1

a B c d

y y y y

1 2 1 2 3 4

1 2 1 2 -2 -1 -2 -1 -2 -1 -1

-1

-2

-1

-2

-1

-2

-1

-2

2

1 2

1

2

1

2

1

3

•

y

H

x

•

A(2, 4)

B(0, -1)

5

2

Slope = =

Slope (m) =

Positive slope because the line is increasing from left to right.

-2

-2

2

the rise

the run

x x x x

If the rise is positive, you move up If the rise is negative, you move down If the run is positive, you move right If the run is negative, you move left

The Evil Slope Man