Most of the graphing resources used shows that the graph is translated up by 3.25 (3 + 1/4). If you add the 3 and the 1/4, you get the equation of a line:
f(x) = x + 3.25,
which means that the graph of f(x)= x now has a y intercept of 3.25.
The graphs are below. The red line represents f(x) = x, and the green line represents (x+3)+1/4. Hope this helps!
Answer:
and
Step-by-step explanation:
Given:
Equation 1:
Simplifying the above equation by dividing both sides by 100
Equation 2:
Simplifying the above equation by dividing both sides by 400.
Now the system of equation is:
(1a)
(2a)
Solving by elimination
Multiplying equation (2a) with
(2b)
Adding equations (1a) and (2b) in order to eliminate
+
We get
∴
Plugging in equation (2a).
Adding both sides.
∴
Answer:
is the amount, in millions, for the number of Apple iPods sold in t years after 2005.
Step-by-step explanation:
Linear function:
A linear function has the following function:
In which m is the slope(the value that y changes by when x changes by 1) and b is the y-intercept(the initial value of the output).
Finding the value in 2005:
This is b.
The number of Apple iPods sold in 2009 was 54.13 million. That number decreased approximately linearly to 26.38 million iPods sold in 2013.
So in 4 years, it decreased from 54.13 - 26.38 = 27.75 million.
So the value in 2005 should also be 27.75 million more than in 2009, that is 54.13 + 27.75 = 81.88. So
Using A for y and t for x
Finding the slope:
When we have two points, the slope is given by the change in the output divided by the change in the input.
In 4 years, the amount decrease by 27.75 million. So
So
is the amount, in millions, for the number of Apple iPods sold in t years after 2005.