Objective- To write a linear equation given a pointand a slope.

Write a linear equation in standard form given:slope = 3 y-intercept = -2

m = 3 b = -2

y = 3x + -2

y = mx + b

Not in standard form!

Ax + By = C-3x -3x

-3x + y = -2 Where A, B and Care integers.or

3x - y = 2

- x + y = -2

- x + y = -2

- x - x

Write a linear equation in standard form given:

slope = y-intercept = -214

y = mx + b

y = x - 214

Not in standard form!

Ax + By = CWhere A, B and Care integers.

14

14

1414 No fractions!4

- x + 4y = -8 or x - 4y = 8

5 x + y =

5

5

Write a linear equation in standard form given:

slope = point = (2,4)-15

y = mx + b

y = x + b-15

(x,y)

4 = (2) + b-15

4 = + b-25

5 5+ + 22

4 = b 25

= 22

y = x +-15

22

5+ x + x11

5

1 225

5

x + 5y = 22

x + y =

7

7

Write a linear equation in standard form given:

slope = point = (1,-2)-37

y = mx + b

y = x + b-3

(x,y)

-2 = (1) + b-3

-2 = + b-37

+ + 37

37

-2 + = b 37

= -117

y = x +-37

-117

+ x + x37

37

37

-117

7

3x + 7y = -11

+ = b 37

-147

55 x + y =5

5

5

Write a linear equation in standard form given:

slope = x-intercept = 435

y = mx + b

y = x + b3

(x,y)

0 = (4) + b3

0 = + b12

- - 5

125

12

= b -12

5

y = x +35

-125

- x - x35

35

-3 -125

-3x + 5y = -12

(4,0)

or

3x - 5y = 12

3

3

31

33

Finding an Equation Given Two Points

Write the equation of the line which contains:(-2, 3) (4, 5)

Slope (m) =y2- y1

x2- x1

y = mx + b

Slope (m) =5 - 3

4 - -2=

26

m =13

y = x + b

(x, y)5 = (4) + b1

5 = + b4

b = 5 - 43

=153

43

-

b =113

y = x + 1 11

411411

4

Write the equation of the line which contains:

(0, -3) (4, 8)

Slope (m) =y2- y1

x2- x1

y = mx + b

Slope (m) = 8 - -34 - 0 =

114

m =114

y = x + b(x, y)

8 = (4) + b

8 = 11 + b-11 -11

-3 = b

b = -3y = x - 3 11

Use the x-y chart below to write a linear equation that satisfies all the points.

x y 2 4

4 10

7 19

9 25

14 40

6

10 - 4m =x2- x1

=4 - 2

m = = 3

y = mx + b

y = 3x + b

10 = 3(4) + b

10 = 12 + b-12 -12

-2 = by2- y1

2

+6

+9

+6

+15

+2

+3

+2

+5

y = 3x - 2

Wat

er L

evel

(G

al.)

Hours

60

50

40

30

20

10

00 1 2 3 4 5

The graph below represents the volume of water in a tank (y) over time (x). Find the equation thatdescribes y in terms of x.

(0,60)

(2,30)

30 60m2 0

302

m 15

15 60y 15x 60

y mx b

2 1

2 1

y ym

x x

Tot

al C

ost

Miles

60

50

40

30

20

10

00 5 10 15 20 25

The graph below represents the total cost of ataxi ride (C) over miles driven (n). Find the equation that describes C in terms of n.

C

n

(0,5)(20,20)

20 5m20 0

1520

m 0.75

0.75 5C 0.75n 5

y mx b

2 1

2 1

y ym

x x

(x )

Point-Slope Form

1 1y y m(x x )

Write the equation of a line in point-slope form that passes through (2,5) with a slope of -3.

1 1y y m(x x ) 1 1(x , y ) m

y 5 3 2

Forms of the Linear Equation

Standard Form Slope-Intercept Form

Point-Slope Form

1 1y y m(x x )

Ax By C

y mx b

3(x )

Write the equation in slope-intercept form that

passes through (-2,6) with slope of 3.

1 1y y m(x x ) y

1 1(x , y ) m

6 2y 6 3(x 2) y 6 3x 6

6 6

y 3x 12

3 (x )5

Write the equation in slope-intercept form that

passes through (5,-1) with slope of .

1 1y y m(x x )

35

1 1(x , y )m

y 1 5

3y 1 (x 5)5

3y 1 x 35

1 1 3y x 4

5

2 (x )3

Write the equation of the line below inslope-intercept form.

x

y

(-2, 3)

1 1y y m(x x )

-2

+3

y 3 2

2y 3 (x 2)3

2 4y 3 x3 3

3 3

2 5y x3 3

2m3