8-5: Standard Form of an Equation
of a Line
Mr. Gallo
Graphing Linear Functions
Given the equation 3x + 2y = 6
Complete the table for the values of x and y:
x
y
3x + 2y = 6
Ordered Pair
0
3
3 0  2 y  6
2
0
3x  2  0   6
4
3
3 4  2 y  6
4
6
 0,3
 2, 0 
 4, 3
 2, 6 
3x  2  6   6

Graph the coordinates on the coordinate plane:
What do you notice about the
coordinates when x = 0 and y = 0?
______________________
Another name for the coordinate when
x = 0 and the coordinate of the point is
(0, y) is the
_______________________
Another name for the coordinate when
y = 0 and the coordinate of the point is
(x, 0) is the
_______________________
Why are these points useful?
The Slope Intercept Form
Standard Form
An equation of the form Ax + By = C is in standard form
when:



A, B, and C are integers
A and B are not both zero, and
A is not negative.
Example 1: Julia bought some CDs that cost $12 each and some DVD’s that
cost $24 each for a total of $120.
Write an equation in standard form that models this situation.
Let x = the number of CDs
Let y = the number of DVDs
How would you represent the cost of x CDs?
How would you represent the cost of y DVDs?
y  3x  1
 y  intercept
y  mx  b
Equation: _____________
1
3
 slope m
b
Write the equation that supports the data:
Graph the equation on the coordinate system:
Write the equation in standard form:
3 1

9 3
Graph the equation on the coordinate system:
1
3
1
3
Example 3 - Graph the
equation y  2 x  5
What is the y-intercept?
_______
 0,5
2
1
What is the slope? ______
Example 4 - Graph the
equation y  2 x  4
What is the y-intercept?
 0, 4
______
2
What is the slope? ______
1
How are the graphs alike?
__________________
They have the same
y  2 x  5
__________________
slopes.
__________________
Parallel lines
__________________
How are they different?
_________________
They
have different
_________________
y –intercepts.
_________________
_________________
y  2 x  4
Example 6- Find the equation of the line passing through
(0, 6) and with slope −4.
Slope: _________.
4
Substitute Point:
y  4 x  b
6  4  0  b
6b
y  4 x  6
Equation: _____________
Example 7: Find the equation for the line passing
through (3, −4) and (9, 0).
2
3
Slope: _________.
y2  y1 0  (4) 4 2
m

 
x2  x1
93
6 3
2
Substitute Point: y  x  b
3
2
0  (9)  b
3
2
0  6b
y  x6
3
6  b
Equation: _____________
Homework: 8.3-8.4 Worksheet