Chapter 5 Writing Linear Equations - The Standard Form Of A Linear Equation Worksheet - Connie Gross
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5.6
The Standard Form
of a Linear Equation
GOAL
1
W
E
S
F
RITING AN
QUATION IN
TANDARD
ORM
What
you should learn
GOAL
Write a linear
1
Most of the linear equations in this chapter are written in slope-intercept form.
equation in standard form.
y = mx + b
Slope-intercept form:
Use the standard
GOAL
2
form of an equation to model
Another commonly used form is the
standard form
of the equation of a line.
real-life situations, such as
the amount of food to
Ax + By = C
Standard (or general) form:
purchase for a barbecue in
Example 4.
In this form, notice that the variable terms are on the left side of the equation and
the constant term is on the right. A, B, and C represent real numbers and A and B
Why
you should learn it
are not both zero.
To model real-life
situations, such as buying
ACTIVITY
combinations of bird seeds
Developing
in Exs. 64–66.
Investigating Forms of Equations
Concepts
Graph each of these equations.
1
4
=
a. y
b. º4x + 3y = º6
c. 4x º 3y = 6
x º 2
3
Which, if any, of the equations are equivalent? How do you know?
2
Writing an Equation in Standard Form
E X A M P L E 1
2
Write y =
x º 3 in standard form with integer coefficients.
5
S
OLUTION
To write the equation in standard form, isolate the variable terms on the left and
the constant term on the right.
2
y =
x º 3
Write original equation.
5
2
5y = 5
x º 3
Multiply each side by 5.
5
5y = 2x º 15
Use distributive property.
º2x + 5y = º15
Subtract 2x from each side.
. . . . . . . . . .
A linear equation can have more than one standard form. For instance, if you
multiply each side of the standard form above by º1, you get 2x º 5y = 15,
which is also in standard form.
308
Chapter 5 Writing Linear Equations
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