1. Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?

2. How do you interpret the slope and y intercept in a real world case?

3. By looking at two linear equations, how can you tell that the corresponding lines are parallel?

4. By looking at two linear equations, how can you tell that the corresponding lines are perpendicular?

5. When graphing a linear inequality, how do you know if the inequality represents the area above the line?

6. What are the necessary and sufficient conditions for inequalities to represent an area in the first quadrant?

7. In which quadrant will the area be if x > 0 and y < 0? Can the area be shifted to a different quadrant simply by using additional inequalities? Why?

8. When solving a linear inequality, why do you always solve for y?

Solution Preview

1) The equation doesn't change just because you choose different points. If those points are both on the line, then generating an equation from those two points will have to result in the same line being graphed. A line stretches forever in both directions; in order for a different graph to appear, at least one point must be off of the original line.

2) The y-intercept is ...

Solution Summary

This answers some questions regarding equations, including real-life applications and how to interpret graphs.

For each of the following ordinairy differential equations, indicate its order, whether it is linear or nonlinear, and whether it is autonomous or non-autonomous.
a) df/dx +f^2=0
(See attachment for all questions)

The techniques for solving linearequations and linear inequalities are similar, yet different. Explain and give an example of both a linear equation and a linear inequality that demonstrates this difference.
1.) Solve and check the linear equation.
5x - 5 = 30
A) {30}
B) {34}
C) {11}
D) {7}
2.) Solve and check th

1. Plot the graph of the equations 3x-8y=5 and 4x-2y=11 and interpret the result.
2. Plot the graph of the equations 4x-6y=2 and 2x-3y=1 and interpret the result.
3. Plot the graph of the equations 10x-4y=3 and 5x-2y=6 and interpret the result.
Show all graphs.

Please see the attached files for the fully formatted problems.
1. Given the equation below, find f(x) where y = f(x).
8y(6x - 7) - 12x(4y + 3) + 265 - 5(3x - y + 2) = 0.
2. Solve these linearequations for x, y, and z.
3x + 5y - 2z = 20; 4x - 10y -z = -25; x + y -z = 5
3. The value of y in Question 2 lies in the ran

1. Juanita sells two different computer models. For each Model A computer sold she makes $45, and for each Model B computer sold she makes $65. Juanita set a monthly goal of earning at least $4000.
A) Write a linear inequality that describes Juanita's options for making her sales goal.
2. The Candy Shack sells a particular

1. You are given the following system of linearequations:
3x - 2y + z = 2
-x + y = 3
-2y + 6 = -1
Provide a coefficient matrix corresponding to the system of linearequations.
What is the inverse of this matrix?
What is the transpose of this matrix?
Find the determinant for this matrix.
Calculate the following