Fifth grade has 24 students per each teacher.
Sixth grade has about 23 students per teacher.
Sixth grade is lower.
Answer:
Part A) see the explanation
Part B) 
Step-by-step explanation:
Part A)
we know that
A relationship between two variables, x, and C, represent a proportional variation if it can be expressed in the form
or 
Let
C ---> is the total cost (represent the output or dependent variable)
x ----> is the number of books (represent the input or independent variable)
In this problem
we have a proportional relationship between the variables x and C
Part B) we know that
The linear equation is given by

The constant of proportionality k is the same that the slope or unit rate of the linear equation
In this problem the constant k is given

so

For x=12 books
substitute in the equation and solve for C

In function notation

Answer:
<h3>y = - 1/2x - 1/2</h3>
Step-by-step explanation:
Equation of line is y = mx + c
where m is the slope
c is the y intercept
Slope of the line using points
(1, -1) and (-3, 1) is

Equation of the line using point
( 1 , - 1) and slope - 1/2 is

Hope this helps you.
Answer:
The graph now opens in the opposite direction. The y intercept is shifted up 4.
Step-by-step explanation:
F(x) = 2x^2-8
F(X)= -2x^2-4
We know that the graph is reflected over the y-intercept becuase of the negative sign in the second equation ( F(X)= -2x^2-4)
We know that the intercept is shifted up four, because the number decreased from 8 to 4, and the graph is reflected.
Attacthed is both of the equations graphed to help you visualize this shift!