Lesson 6-3
Standard Form of a
Linear Equation
What is Standard Form?
• Ax + By = C
– It’s when your x’s and y’s are on the
same side equal to a number. Your x
must be positive! x goes first!
Why do we have to know
Standard Form?
• Standard Form is REALLY easy to
graph is you use x- and y-intercepts.
• X-intercept is where the graph
crosses the x-axis.
• Y-intercept is where the graph
crosses the y-axis.
What are the coordinates?
• When
something
crosses the xaxis, what is the
coordinate?
• (x, 0) The y is
always zero.
5
4
3
2
1
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
• When
something
crosses the yaxis, what is
the
coordinate?
• (0,y) The x is
always zero.
How to graph using
Standard Form:
Find the y-intercept.
Find the x-intercept.
• Plug in zero for y.
• Ex. 2x + 3y = -2
2x + 3(0) = -2
2x + 0 = -2
2x = -2
x = -1
• Plug in zero for x.
• Ex. 2x + 3y = -2
2(0) + 3y = -2
0 + 3y = -2
3y = -2
y = -2/3
5
4
3
2
1
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
You try…Graph 3x + 4y = 8
X-int…plug in 0 for y
3x + 4(0) = 8
3x + 0 = 8
3x = 8
X = 8/3 or 2.6666666666
Y-int…plug in 0 for x
3(0) + 4y = 8
0 + 4y = 8
4y = 8
Y=2
5
4
3
2
1
Now graph it! 
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
You try…Graph -4x + 3y = 12
X-int. (y=0)
-4x = 12
Divide by -4
X = -3
Y-int. (x=0)
3y = 12
Divide by 3
Y=4
5
4
3
2
1
Now graph it! 
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
Weird Graphs
y = 4
• Where does it cross the
y-axis?
x = -2
• Where does it cross the
x-axis?
5
5
4
4
3
3
2
2
1
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
1
2
3
4
5
-5
-4
-3
-2
-1
0 1
-1
-2
-3
-4
-5
2
3
4
5
Classwork/Homework
pg. 301
2-18 even, 23-26 all
If you think this is
confusing and you’re more
comfortable with y=mx+b,
then change
standard to y=mx+b!
It’s easier than you think…
Convert Into Slope-Intercept Form
2 y  4x  2
(divide both sides by 2 to get y alone)
2 y  4x  2
2
2
(now simplify all fractions)
y  2x 1
*** Check Your Answer ***
-3y = -9x - 12
-3
-3
(divide both sides by -3 to get y alone)
(now simplify all fractions)
-3y = -9x - 12
-3
-3 -3
y = 3x + 4
Slope = 3
Intercept = 4
*** medium ***
Convert to Slope-Intercept Form:
21x – 7y =14
(subtract both sides by 21x)
21x
-21x
(now divide both sides by -7)
-7y = -21x + 14
7 - 7 -7
y = 3x – 2
(simplify all fractions)
Now you should be able to:
• Define standard
form
• Define x- and yintercepts
• Know how to solve
the standard form of
a linear equation for
the x- and yintercepts
• Graph using x- and
y-intercepts
• Change standard
form to y=mx+b
form then graph
the linear equation
from there