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Lines, Lines, Lines!!!
~
Standard Form
Another equation of the
same line.
What we Have Learned
so far….
Slope Intercept Form
y  mx  b
Where m is the slope and b
is the intercept
What we Have Learned
so far….
Point-Slope Form
y  y1 mx  x1 
Where m is the slope and
x1,y1  are a point on the line.
We will use our prior knowledge of
Slope-Intercept Form
&
Point-Slope Form
To learn about the Standard Form of a Line:
Ax + By = C
Standard Form
The Standard Form of a Linear Equation is
Ax + By = C
Where A ≥ 0,
&
A and B are not both zero
&
A, B, and C are integers whose greater common
factor is 1.
Standard Form
The Standard Form of a Linear Equation is
Ax + By = C
Notice that:
 x and y have exponents of 1
 x and y are not multiplied together
 x and y do not appear in denominators,
exponents, or radicals
Examples of Standard Form
These Equations are
in Standard Form:
2x + 5y = 7
x – y = - 10
1000x + 75y = 6
These Equations are
not in Standard Form:
1/2x + 2/3y = 6
12x – 36y = 10
5ix + 7py = -29
Question:
Is the equation 4x + 7y = -10 a linear
equation? Explain why.
This equation is a linear equation because it is in
standard form with A = 4, B = 7, and C = –10.
Is the equation
Explain why.
2xy = 4 a linear equation?
This equation is not a linear equation because x
and y are multiplied by each other.
Writing an equation in Standard Form
Ax + By = C
y = 2/5x - 3
(5)y = (2/5x - 3)5
5y = 2x - 15
5y -2x = 2x -2x – 1
-2x + 5y = -15
-1(-2x + 5y = -15)
2x – 5y = 15
A= 2, B= -5, and C = 15
Writing an equation in Standard Form
Ax + By = C
Given A Point and a Slope
Point (3,4) and m = 6
y - y1 = m(x - x1)  Use Point-Slope Form
y - 4 = 6(x - 3)  Substitute the values
y - 4 = 6x – 18  Use Distributive Property
y - 4 + 4 = 6x - 18 + 4  Add Liked Terms
y = 6x – 14  Slope-Intercept Form
-6x + y = 6x – 6x – 14  Move the x value
-6x + y = -14  Add Liked Terms
-1(-6x + y = -14)  Multiply times -1
6x – y = 14  Standard Form
Writing an equation in Standard Form
Ax + By = C
Given Two Points (6, -2) and (-4, 4)
First: Find the Slope between the two
points
Second: Use the Slope and the first point on
the Point-Slope Form. Plug them in.
Writing an equation in Standard Form
Ax + By = C
Given Two Points (6, -2) and (-4, 4)
 A = 3, B = 5 and C = 28
Steps to Graph Equations in standard form
1.Write the equation in standard form
2.Find x-intercept, by letting y = 0, solve for x, plot the point where x crosses the x-axis
3.Find y-intercept, by letting x = 0, solve for y, plot the point where y crosses the y-axis
4.Draw a line through the 2 points.
Graph 2 x + 3 y = 12
1.Already using standard form: 2 x + 3y = 12
2. Let y = 0
2 x + 3(0) = 12
2x
= 12
x
= 6
x-intercept is at ( 6 , 0 )
(0,4)
3. Let x = 0
2 (0) + 3 y = 12
3 y = 12
y= 4
y-intercept is at ( 0 , 4 )
•
•
(6,0)
Your Turn!
How do you graph a line which is in
standard form?
Graph 3x - 4y = -12
4
x y
0 3
(3)0 - 4y = -12
-4 0
3x - (4)0 = -12
2
Graph the points and
connect the dots
-5
5
-2
-4
Student Activity
You will now receive a
worksheet. Turn the
worksheet in when
completed.
Do Not Disturb
Work In Progress