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5.5 Writing Equations in Point-Slope Form

• Write the equation of a line in point-slope form.

• Write linear equations in different forms

What we Know so far….What we Know so far….

Slope Intercept Form

bmxy

Where m is the slope and b is the intercept

The New Stuff… Point- Slope The New Stuff… Point- Slope FormFormPoint- Slope form is:

)( 11 xxmyy Where m is the slope

and (x1,y1) is the given point

Point Slope Form

Write the equation of the line with slope 3 and passing through the point (1, 5).

y – y1 = m(x – x1)

135 xy335 xy

533 xy

23 xy

Write the equation of the line with slope ¾ and passing through the point (-5, 3).

y – y1 = m(x – x1)

)5(3 43 xy

415

433 xy

412

415

43 xy

427

43 xy

53 43 xy

Write the equation of the line with slope -4/7 and passing through the point (2, -4).

y – y1 = m(x – x1)

2)4( 74 xy

78

744 xy

728

78

74 xy

720

74 xy

24 74 xy

Write the equation of the line passing through the points (-2, 6) and (3, -1).

y – y1 = m(x – x1)

3)1( 57 xy

55

521

57 xy

516

57 xy

521

571 xy

xym

)2(361

m

57m

Write the equation of the line passing through the points (4, 3) and (6, 8).

y – y1 = m(x – x1)

43 25 xy

3103 25 xy

725 xy

103 25 xy

xym

4638

m

25m

Write the equation of the line passing through the points (4, -3) and (-7, -1).

y – y1 = m(x – x1)

4)3( 112 xy

1133

118

112 xy

1125

112 xy

118

1123 xy

xym

47)3(1

m

112

m

112m

Why does the point-slope form work?

xym

1

1

xxyym

Find the slope between (x1, y1) and (x, y).

11 yyxxm

11 xxmyy

1xxbysidesbothmultiply

1xx 1xx

Convert y = 3x + 2 to standard form.

23 xy

23 yx

23 yx

)1(231 yx

Convert to standard form.

427

43 xy

427

43 yx

2743 yx

)4(4 427

43 yx

427

43 xy

Convert to standard form.

716

74 xy

716

74 xy

716

74 yx

1674 yx

)7(7 716

74 yx

716

74 xy

Write the equation of the line parallel the line 4x – 5y = 7 that passes through the point (-3, 7)

754 yx

745 xy

57

54 xy

54m

y – y1 = m(x – x1)

)3(7 54 xy

535

512

54 xy

547

54 xy

512

547 xy

37 54 xy

Write the equation of the line perpendicular the line

3x + 2y = 9 that passes through the point (2, 5)

923 yx

932 xy

29

23 xy

23m

y – y1 = m(x – x1)

25 32 xy

315

34

32 xy

311

32 xy

34

325 xy

32m