STUDENT HELP
Look Back
For help with solving
linear equations, see
p. 155.
EXAMPLE 2
Writing a Linear Equation
Write the standard form of an equation of the line passing through (º4, 3) with
a slope of º2.
SOLUTION
You are given a point on the line and its slope, so you can write the point-slope
form of the equation of the line.
y º y1 = m(x º x1)
Write point-slope form.
y º 3 = º2[x º (º4)]
Substitute for y1, m, and x1.
y º 3 = º2(x + 4)
Simplify.
y º 3 = º2x º 8
Use distributive property.
2x + y = º5
䉴
Add 2x and 3 to each side.
The equation 2x + y = º5 is in standard form.
EXAMPLE 3
Horizontal and Vertical Lines
Write the standard form of an equation
y
a. of the horizontal line.
(2, 3)
b. of the vertical line.
1
5
SOLUTION
(3, 1)
a. The horizontal line has a point with a
1
1
1
3 x
y-coordinate of 3. The standard form of
the equation is y = 3.
b. The vertical line has a point with an
x-coordinate of º3. The standard form
of the equation is x = º3.
..........
You have now studied all of the commonly used forms of linear equations. They
are summarized in the following list.
CONCEPT
SUMMARY
E Q UAT I O N S O F L I N E S
SLOPE-INTERCEPT FORM:
y = mx + b
POINT-SLOPE FORM:
y º y1 = m(x º x1)
VERTICAL LINE (UNDEFINED SLOPE):
x=a
HORIZONTAL LINE (ZERO SLOPE):
y=b
STANDARD FORM:
Ax + By = C, where A, B, and C
are real numbers; A and B are not
both zero.
5.6 The Standard Form of a Linear Equation
309