MATHPOWERTM 10, WESTERN EDITION

Equations of Linear RelationsLesson 4 -5

6.5.1

When the equation of a line is written in the formAx + By + C = 0, the equation is in Standard Form.For an equation to be in standard form:

To write an equation of a line, you need:1. the slope of the line2. a point on the line

• A, B and C are integers.• A is a positive integer.• A and B cannot both be zero.

6.5.2

Writing Equations in Standard Form

y - y1 = m(x - x1)

The equation y - y1 = m(x - x1)is the point-slope form.More useful like this:

Use the slope formula where:•(x, y) represents any point on the line, and •(x1, y1) refers to the given point.

Writing the Equation of a Line

6.5.3

1

1

xx

yym

1

1

xx

yym

Write an equation in standard form for the line through(6, -2) with slope of .

3x - 4y - 26 = 0

2x + 3y - 17 = 0

(x1, y1)

6.5.4

34

Writing an Equation Given a Point and a Slope

Write an equation in standard form for the line through(-2, 7) with slope of .

-23

Standard form of the equation

1

1

xx

yym

62

4

3

x

y

84183 yx

2463 yx

081843 yx

3

2

2

7

x

y

42213 xyStandard form of the equation is

Find the equation, in standard form, of the line that passes through the points A(3, -4) and B (5, 6)

m y2 y1

x2 x1

m 6 ( 4)

5 3

m 10

2

m = 5

6.5.5

Using the point B(5, 6):

Using the point A(3, -4):

Writing an Equation Given Two Points

1

1

xx

yym

3

4

1

5

x

y

4155 yx5x - y - 19 = 0

1

1

xx

yym

5

6

1

5

x

y

6255 yx

5x - y - 19 = 0

Find the equation of a line that is Parallel to the

m y2 y1

x2 x1

m 5 0

0 5

m = -1

(0, 5)

(5, 0)

6.5.6

Writing the Equation from the Graph

1

1

xx

yym

0

51

x

y

50

5

yx

yx