# Algebra for Value Equations

Please help me solve this problem.

Given the equation: y = |2x - 1| + 1

Absolute value equations involving linear powers of x result in two lines which cross each other.

1. What are the equations of the two lines from the absolute value equation?

y1 = m1x1 + b1 and y2 = m2x2 + b2

2. Plot these two lines on a piece of graph paper.

3. What are the coordinates of the crossing point?

4. There are 4 half-lines which project out from the crossing point. Clearly mark which of the two half-lines constitute the answer to the absolute value equation. (Make the half-lines thicker and darker.)

5. What are the x-intercepts of your answer? (Write "none" if there are no x-intercepts.)

6. What are the y-intercepts of your answer? (Write "none" if there are no y-intercepts.)

7. What is the domain of x when y is increasing? (use interval notation)

8. What is the range of y when y is increasing?

9. What is the domain of x when y is decreasing?

10. What is the range of y when y is decreasing?

11. Let the absolute value equation be changed to

y < |2x - 1| +1.

Then shade in the area of the answer on your graph.

https://brainmass.com/math/linear-algebra/algebra-value-equations-612519

#### Solution Summary

The expert determines the equations of the two lines from the absolute value equation.