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Questions about Linear Equations

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.

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