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8 Standard Form of Equation.notebook April 07, 2017
Opener:
Cars Washed
Money$
5 40
10 80
15 120
20 160
The local Scouts held a car wash as a fundraiser. Below is the money they made. Write the equation relating the money they made to the number of cars washed. Is the relationship linear?
Groups:
1 Jozef, Sofia
2 Haley, Garrett, Ava
3 Chris, Harper
4 Sydney, Ben
5 Liam, Nic
8 Standard Form of Equation.notebook April 07, 2017
2. An experiment was set up to determine the rate of evaporationof water from an open container. The following data was obtained.a) find the rate of evaporationb) find the equation relating the time and water remaining in the containerc) graph the data
Timehours
VolumemL
0 40
5 37.5
10 35
15 32.5
8 Standard Form of Equation.notebook April 07, 2017
The arctic tundra is home to a variety of mammal species.
A variety of mammal species live in the arctic tundra.
Do these statements have the same meaning?
Where is the emphasis placed in each statement?
With your shoulder partner, create a series of similar statements. Be prepared to share your answer!
8 Standard Form of Equation.notebook April 07, 2017
We can do something similar with the equation of a line.
Where is the emphasis in y = mx + b?
This is called the slope yintercept form
Ax + By + C = 0 is the equation of a line in standard form.
A, B, and C are integers.
A and B are both not zero.
8 Standard Form of Equation.notebook April 07, 2017
One more thing...In standard form, the coefficient of the xterm is always positive!
What can we do if this coefficient is negative?
3x + 4y 7 = 0
8 Standard Form of Equation.notebook April 07, 2017
The equation 9C 5F +160 = 0 describes the relationship between temperature in degrees Celsius (C), and temperature in degrees Fahrenheit (F)
a. Express this equation in the form C = mF + bb. What is the rate of change for this equation? What does it mean?
c. Identify the Cintercept. What does it mean?
8 Standard Form of Equation.notebook April 07, 2017
d. express the equation in the form F = mC + b.e. What is the rate of change for this equation? What does it mean?
f. What is the Fintercept? What does it mean?
Compare the graphs of the 2 relations you just worked with.
How are they the same?
How are they different?
How are the slopes of the two graphs related?
8 Standard Form of Equation.notebook April 07, 2017
8 Standard Form of Equation.notebook April 07, 2017
Standard Form of a Linear Equation Ax +By +C = 0
At times, an equation is written in standard form.
Example1: x + y + 5 = 0
a) Fill in the values for the tableb) graph the datac) find the slope and yinterceptd) Write the equation in y = mx+ b form
x x + y + 5 = 0
5
3
1
0
1
3
8 Standard Form of Equation.notebook April 07, 2017
Could we find the equation of the line in y = mx + b form without graphing?
Ex1. x + y + 5 = 0 Use algebra!
Ex2. 3x y 12 = 0
8 Standard Form of Equation.notebook April 07, 2017
Ex 3: 10x + 5y 15 = 0
a) Write the equation in y = mx+ b formb) graph the equation using yintercept and slope
8 Standard Form of Equation.notebook April 07, 2017
y=mx + b Ax +By + C = 0
1. Rearrange the equation y = 3x 2 into standard form
2. Rearrange the equation y = x + 5 into standard form
8 Standard Form of Equation.notebook April 07, 2017
Homework: page 100 #1 all, #2 choose 2page 10 #10 a,c,e
