8-5: Standard Form of an Equation of a Line
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8-5: Standard Form of an Equation of a Line Mr. Gallo
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8-5: Standard Form of an Equation of a Line. Mr. Gallo. Graphing Linear Functions. Given the equation 3 x + 2 y = 6 Complete the table for the values of x and y :. What do you notice about the coordinates when x = 0 and y = 0 ? - PowerPoint PPT Presentation
Transcript of 8-5: Standard Form of an Equation of a Line
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
0
4
6
3 0 2 6y 3 0,3
3 2 0 6x 2 2,0
3 4 2 6y 3 4, 3
3 2 6 6x 4 2,6
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 FormStandard 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 bmx Equation: _____________
mb
slope
y intercept
31
3 1y x
Write the equation that supports the data: Graph the equation on the coordinate system: Write the equation in standard form:
Graph the equation on the coordinate system:
3
9
1
3
1
3
1
3
Example 3 - Graph the equation
What is the y-intercept?_______ What is the slope? ______
Example 4 - Graph the equation
What is the y-intercept?______ What is the slope? ______
0,52
1
0, 42
1
2 4y x
2 5y x
How are the graphs alike?
____________________
____________________
____________________
____________How are they different?
___________________
___________________
___________________
___________
2 4y x
2 5y x They have the
same slopes.
They have
different y –
intercepts.
Parallel lines
Slope: _________.
Example 6- Find the equation of the line passing through (0, 6) and with slope −4.
4y x b
Equation: _____________
4
64y x
Substitute Point:
6 04 b
6 b
Example 7: Find the equation for the line passing through (3, −4) and (9, 0).
2
3y bx
Equation: _____________
36
2y x
Slope: _________.
Substitute Point:
2 1
2 1
y ym
x x
0 ( 4)
9 3
4
6
2
3
2
3
0 (2
39) b
0 6 b 6 b
Homework: 8.3-8.4 Worksheet
