Expert Sheet 1 “Transposing a Linear Equation into Standard form”

Answer Key Example 1. Transpose the equation into standard

form.

2x + y = -8

-2x -2x

y = -2x – 8

Standard form: y = -2x – 8

m = -2

1 b = -8

m represents the slope

b represents the y-intercept

Example 2. Transform the equation into standard

form.

y = mx + b

12 + 3y = 9x

-12 -12

3y = 9x – 12

3 3 3

y = 3x – 4

Standard form: y = 3x – 4

m = 3

1 b = -4

m represents the slope

b represents the y-intercept

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

*the y-intercept (b) is zero.

m = _______ b = ________

Lnhotsoubanh/jigsaw/linear

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.

3 -6

y = mx + b 3y = 4x – 9 3 3 3

y = 4x – 3

3

4 3 -3

y = mx + b y + 2x = 10 -2x -2x

y = -2x + 10

-2 10

y = mx + b x – y = 4

-x -x -y = -x + 4 -1 -1 -1

1 -4

y = mx + b

3x – 9y = 18 -3x -3x

-9y = -3x + 18 -9 -9 -9

y =

x – 2

1

3 -2

mx + b = y

x = 5y 5 5

y =

x

1

5 0

y = mx + b 6 + y = 3x -6 -6

y = 3x + 6

Expert Sheet 2

“Write an Equation of a Line”

Answer Key

Ex1. Write an equation of a line that has a slope of 5

2

and y intercept of 3.

y = mx + b

Equation: y =5

2x – 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 2

3

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.

y = mx + b

0 = -1(3) + b

0 = -3 + b 3 = b

Equation: _____________________________

7. Write an equation of a line that has a slope of 6 and

a x-intercept of 0.

y = mx + b

0 = 6(0) + b

0 = b

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

y = x + 4 y = 8

y = -x + 3 y = 6x

Expert Sheet 3

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

Answer Key

Directions: Find the equation of a line that passes through the given points.

1.) (-3, -4) and (2, 11)

m = y1

- y2

x1

- x2

m = 35

15

23

114

y = mx + b 11 = 3(2) + b

11 = 6 + b

-6 -6

5 = b

Answer: y = 3x + 5

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

m = y1

- y2

x1

- x2

m = 3

2

12

8

66

135

y = mx + b

-5 = (-6) + b

-5 = 4 + b

-4 -4

-9 = b

Answer: y = x – 9

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

m = y1

- y2

x1

- x2

m = 06

0

60

22

y = mx + b

2 = 0(0) + b 2 = 0 + b

2 = b

y = 0x + 2

Answer: y = 2 horizontal line, slope is zero

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

m = y1

- y2

x1

- x2

m = undefined0

11

-10)10-

-4)7

(

(

Answer: x = -10

vertical slope, therefore there is no slope and no

y-intercept

(x, y) (0, 2)

(6, 2)

(x, y)

(-10, 7)

(-10, -4)

(x, y)

(-3, -4)

(2, 11)

(x, y)

(-6, -5) (6, -12)

(pick one of the points to

substitute in for x & y)

(pick one of the points to

substitute in for x & y)

(pick one of the points to

substitute in for x & y) (pick one of the points to

substitute in for x & y)

Expert Sheet 4

“Write an Equation of a Line, Given a Graph”

Answer Key

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 = 5

4. Line B: ________________________

Slope (m) = undefined y-intercept = none

5. Line C: ________________________

Slope (m) = ______ y-intercept = -3

6. Line D: ________________________

Slope (m) = ______ y-intercept = 3

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

-1 5

y =

x = 4

y =

y =

4 2

= 2

1 3

Expert Sheet 5

“Write an Equation of a Line, Given a Table”

Answer Key

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) = valus- xthe in pattern

values-y the in pattern 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 = 3

2 (-3) + b

6 = 2 + b

-2 -2

4 = b

Function (equation): y = 3

2x + 4

x y

-3 6

0 4

3 2

6 0

9 -2

Now it’s your turn:

3.

y = mx + b Point (2, 0)

0 = -4(2) + b

0 = -8 + b

+8 +8

8 = b

Function (equation): y = -4x + 4

x y

-2 16

2 0

6 -16

10 -32

14 -48

4.

(x, y)

y = mx + b Point (0, 1)

1 = 3

5 (0) + b

1 = 0 + b

1 = b

Function (equation): y = 3

5x + 1

x y

0 1

6 -9

12 -19

18 -29

24 -39

5.

(x, y)

y = mx + b Point (8, 37)

37 = 5(8) + b

37 = 40 + b -40 -40

-3 = b

Function (equation): y = 5x – 3

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

Substitute (x, y) into the equation

y = mx + b

Substitute (x, y) into the equation

y = mx + b

=

Substitute

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

Substitute

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