5.5 Standard Form of a Linear
Equation
Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.FIF.C.7, HS.F-LE.A.2): The student will understand that linear relationships
can be described using multiple representations.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
· Make
connection with
other concepts
in math
· Make
connection with
other content
areas.
The student will
understand that linear
relationships can be
described using multiple
representations.
- Represent and solve
equations and
inequalities graphically.
- Write equations in
slope-intercept form,
point-slope form, and
standard form.
- Graph linear
equations and
inequalities in two
variables.
- Find x- and yintercepts.
The student
will be able
to:
- Calculate
slope.
- Determine
if a point is a
solution to an
equation.
- Graph an
equation using
a table and
slopeintercept
form.
With help
from the
teacher, the
student has
partial
success with
calculating
slope,
writing an
equation in
slopeintercept
form, and
graphing an
equation.
Even with
help, the
student has no
success
understanding
the concept
of a linear
relationships.
Standard or General
Form:
Ax + By = C
Where A, B and C are numbers
x and y are the variables
A and B are called coefficients
3 Rules for Standard
Form
1. Get the variables on the left and the
constant on the right!
2. You must have the leading coefficient as a
positive integer
3. You must have all numbers A, B and C as
integers (whole numbers)
How to change from slopeintercept form to Standard
form

Step 1: Clear out any fractions or decimals by
multiplying all numbers by the denominator or
by the place value of the decimal.

Step 2: Move the x and y variable to the left
side. Keep the constant on the right side.

Step 3: Make sure the x coefficient is
positive. If not, multiply all terms by -1.
Practice:







y=¾x+2
(4)y = (4)¾ x + (4)2
Get rid of fractions.
4y = 3x + 8
-3x -3x
Move all variables to the left.
-3x + 4y = 8 Make first coefficent positive.
(-1)(-3x) + (-1)(4)y = (-1)(8)
3x – 4y = -8
What about decimals?




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
y = -0.24x - 5.2
Multiply through by 100 to clear decimals, then
put in standard form.
(100)y = (100)(-0.24) – (100)(5.2)
100y = -24x – 520
24x + 100y = -520 (Now reduce if possible.)
24x + 100y = -520
4
4
4
6x + 25y = -130
Real-life example:


You have $6.00 to use to buy apples and
bananas. If bananas cost $.49 per pound, and
apples cost $.34 per pound, write an equation
that represents the different amounts of each
fruit you can buy. Graph it.
Let x = bananas and y = apples
.49x + .34y = 6



Since we are using standard form, we will
multiply through by 100 to clear out
decimals.
Therefore:
49x + 34y = 600
What do we do now to graph this?
x-intercept (12, 0)
and y-intercept
(0, 18)
The graph will be
in the first
quadrant only.
Apples
18
Find the x and y intercepts.
12
Bananas
Practice:

Put in standard form the line
passing through point (2, -3)
with a slope of 3.


3x – y = 9
Put in standard for the
horizontal line going through
point (-2, 6)

y = 6