SECTION 5.6
“Standard Form”
WHAT’S IMPORTANT:
-- Be able to write a linear equation in
standard form.
-- Be able to use the standard form of a
linear equation to model real-life situations.
Standard Form
Equations can be written in slope-intercept
form, point-slope form, or standard form.
 For example, here are three equations that
can be written for the line that contains the
points (-3,4) and (0,10).
 Slope-Intercept: y = 2x + 10
 Point-Slope Form: y – 4 = 2(x + 3)
 Standard Form: 2x – y = -10

What is standard form?
 STANDARD
FORM OF A LINEAR
EQUATION:
 Ax + By = C
Steps (Important)
 Step
1: If there is a fraction
coefficient multiply the entire
equation by the denominator.
 Step 2: Simplify
 Step 3: Get x and y on the right
side of the equation.
Example 1:
𝟑
x
𝟒
Write y =
– 2 in standard form with
integer coefficients.
Example 2
𝟏
x
𝟑
Write y =
+ 4 in standard form with
integer coefficients.
Write in standard form given
point and slope. STEPS:
 Step
1: Write in point-slope form.
y – y1 = m(x – x1)
 Step 2: Distribute
 Step 3: Get x and y on the right
side of the equation
Example 3
Write standard form: line passing
through (5,-8) with a slope of -3.
Use integer coefficients.



Step 1: Write in pointslope form.
y – y1 = m(x – x1)
Step 2: Distribute
Step 3: Get x and y on
the right side of the
equation
Example 3
Write standard form: line passing
through (3, 2) with a slope of 4.
Use integer coefficients.



Step 1: Write in pointslope form.
y – y1 = m(x – x1)
Step 2: Distribute
Step 3: Get x and y on
the right side of the
equation
Horizontal Lines
 Horizontal
Lines: y = b
Ex. Line passes through (-3, 4)
y=4
Horizontal Lines
Ex 2: Line passes through (-1, -7)
Vertical Lines
 Vertical
Lines: x = a
Ex. Line passes through (-1, 5)
x = -1
Vertical Lines
Ex 2: Line passes through (3, -2)
Real Life Situation

Example: You are in charge of buying soda and
water for the school picnic. A case of soda costs
$6.00 and a case of water costs $5.00. You
have $48 dollars to spend. Model the possible
combinations water and soda.
Step 1: Write Equation
Real Life Situation
Example: You are in charge of buying soda and
water for the school picnic. A case of soda costs
$6.00 and a gallon of spring water costs $2.00.
You have $48 dollars to spend. Model the
possible combinations water and soda.
Step 2: Make table

Soda (x) 0
Water (y)
1
2
3
4
5
6
7
8
Example 2
You are in charge of buying prizes for a
school contest. A small trophy costs $8 and
a plaque costs $10. You have $40 to spend.
Model the possible combinations of trophies
and plaques.
a) Write Equation
b) Make Table
