13.7 – Writing Linear Equations

y=mx+b What does the m represent?

What does the b represent?

Name the slope and y-intercept of each line

m b

BLUE

GREEN

PURPLE

5

1

2

3

2

1

2

0

2

SLOPE!!! Y-INT!!!

Y

We are going to learn how to write equations.

There are three main types.

1) Slope and y-intercept

2) Slope and a point

3) Two points

12 :int-y5

2- :slope

: whenline theofequation an Write

5

2-

12 xy m b

4

1- :int-y

2

1 :slope

: whenline theofequation an Write

2

1

xy m b

1 :int-y

0 :slope

: whenline theofequation an Write

0 xy m b

1

4

1-

line. thisofequation theWrite

Y - I N T = 3

m = 1

y = 1 x + 3

Solve for y, change it to ‘y =‘

)1(32 xy

Distribute

Get y by itself

332 xy22 13 xy

)62(3

27 xy

43

47 xy

77

113

4 xy

We are going to learn how to write equations.

There are three main types.

1) Slope and y-intercept

2) Slope and a point

3) Two points

Slope-intercept formPoint-slope form

bmxy )( 11 xxmyy Plug in the slope and the point into point slope form

Writing an equation given a slope and a point.

Solve for y (get y by itself)

Plug in the slope and the point into point slope form

3

2m (-6,1)

11 yx)( 11 xxmyy 1 –6 2

3

43

21 xy

11

53

2 xy

Slope-intercept form

Point-slope form

bmxy )( 11 xxmyy

Write the equation of the line given a point and a slope in point-slope form

2

1m (4,2)

11 yx)( 11 xxmyy 2 41

2

Standard form CByAx

Slope-intercept form

Point-slope form

bmxy )( 11 xxmyy

Write the equation of the line given a point and a slope in SLOPE-INTERCEPT FORM

2

1m (4,2)

11 yx)( 11 xxmyy 2 41

2

22

12 xy

22

xy2

1

Standard form CByAx

SLOPE = m =y2 – y1

x2 – x1

Find points and label

Plug into formula

Reduce Fraction

(3,-1) (2, 3)

x1 y1 x2 y2

x2 x1

y1y2

2 3

-13

4-1

Find points and label

Plug into formula

Reduce Fraction

(0, 2) (2, -4)

x1 y1 x2 y2

x2 x1

y1y2

2 0

2-4

-62

4 3

We are going to learn how to write equations.

There are three main types.

1) Slope and y-intercept

2) Slope and a point

3) Two points

One new thing:

Find your own darn slope!

ADJ:AJDSAK:JFDS:FJIJOWEJC:DSJK:FJKOWEIJFKSD:EJIFLSJFKSLFJSKFLJSFELIWPOWPJDPWAOJLJFSLSDEFPWOPEFJSLKFJWPEJFSDLFJSLOPEDSJFKL:WJPAFJPDSVOJDSPKFEIWLPJFKLSDFJ:AJWPVDSNFELWKGJWLEGIJLRIJGDFI

Slope-intercept form

Point-slope form

bmxy )( 11 xxmyy

1) Find slope

2) Take slope, ANY POINT

3) Change into correct form

m =y2 – y1

x2 – x1

(3,-1) (2, 3)

x1 y1 x2 y2 x2 x1

y1y2

2 3

-13

4-1

4

)( 11 xxmyy 3 2 -4

843 xy33 114 xy

Standard form CByAx

Slope-int

Slope-intercept form

Point-slope form

bmxy )( 11 xxmyy

1) Find slope

2) Take slope, ANY POINT

3) Change into correct form

m =y2 – y1

x2 – x1

(-4,1) (6, -4)

x1 y1 x2 y2x2 x1

y1y2

6 -4

1-4

-510

2

1

)( 11 xxmyy 1 –4 -12

22

11 xy

11

12

1 xy

Standard form CByAx

Slope-int

Slope-intercept form

Point-slope form

bmxy )( 11 xxmyy

1) Find slope

2) Take slope, ANY POINT

3) Change into correct form

m =y2 – y1

x2 – x1

(0,5) (6, 7)

x1 y1 x2 y2x2 x1

y1y2

6 0

57

26

3

1

)( 11 xxmyy 5 0 13

xy3

15 )(3

xy 153

Standard form CByAx

Standard yx 315

• Practice problems

Slope – Int Standard

(3, 4); (1, 2) (-2, 4) (1, -5)

• HW #55: Pg 555: 8, 10, 17 – 20 (slope-int and standard) 22, 23, 25 – 30 (even standard, odd slope-intercept), 33 – 38. (20 problems, end problems not easy)– Hint for 33, think circumcenter.