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Chapter 6 Coordinate Geometry
6.5
MATHPOWERTM 10, WESTERN EDITION 6.5.1
Writing Equations in Standard Form
When the equation of a line is written in the form
Ax + By + C = 0, the equation is in Standard Form.
For an equation to be in standard form:
A, B and C are integers.
A is a positive integer.
A and B cannot both be zero.
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To write an equation of a line, you need:
1. the slope of the line
2. a point on the line
6.5.2
Writing the Equation of a Line
y - y1 = m(x - x1)
y  y1
m
x  x1
Use the slope formula where:
•(x, y) represents any point on the
line, and
•(x1, y1) refers to the given point.
The equation y - y1 = m(x
is the point-slope form.
- x1)
6.5.3
Writing an Equation Given a Point and a Slope
Write an equation in standard form for the line through
(6, -2) with slope of 3 .
(x1, y1)
4
y - y1 = m(x - x1)
3
y - (-2) = (x - 6)
4
3
y
(-2)
=
4[
4[
]
(x - 6) ]
4
4(y + 2) = 3(x - 6)
4y + 8 = 3x - 18
0 = 3x - 4y - 26
3x - 4y - 26 = 0
Standard form of the equation
Write an equation in standard form for the line through
(-2, 7) with slope of -2.
2x + 3y - 17 = 0
3
6.5.4
Writing an Equation Given Two Points
Find the equation, in standard form, of the line that
passes through the points A(3, -4) and B (5, 6).
y 2  y1
m
x2  x1
6  (4)
m
53
10
m
2
m=5
Using the point B(3, -4):
y - y1 = m(x - x1)
y - (-4) = 5(x - 3)
y + 4 = 5x - 15
0 = 5x - y - 19
5x - y - 19 = 0
Using the point B(5, 6):
y - y1 = m(x - x1)
y - 6 = 5(x - 5)
y - 6 = 5x - 25
0 = 5x - y - 19
5x - y - 19 = 0
6.5.5
Writing the Equation from the Graph
(0, 5)
(5, 0)
y 2  y1
m
x2  x1
50
m
05
m = -1
y - y1 = m(x - x1)
y - 0 = -1(x - 5)
y = -x + 5
x+y-5=0
6.5.6
6.5.7
Suggested Questions:
Pages 282 and 283
1 - 13 odd, 17,
21, 27, 29, 32
37 - 40, 46, 49,
50, 52, 53