Question

Y=2 | n-3 | ; Find W(-3)
Answer should be 12

Answer 1

Given the expression \( Y = 2 | n - 3 | \), we can derive \( W(-3) \) by inserting \( n = -3 \) into the expression.

1. Substitute \( n = -3 \):
\[
Y = 2 | -3 - 3 |
\]

2. Simplify the expression inside the absolute value:
\[
Y = 2 | -6 |
\]

3. Calculate the absolute value:
\[
Y = 2 \times 6
\]

4. Multiply:
\[
Y = 12
\]

Thus, \( W(-3) = 12 \), which matches the answer you provided.

Answer 2

Would this be a linear equation or no?

Answer 3

The equation \( Y = 2 | n - 3 | \) is not a linear equation because it involves an absolute value expression.

### Characteristics of Linear Equations:
- A linear equation can be expressed in the form \( Y = mx + b \), where \( m \) and \( b \) are constants, and \( x \) represents the variable.
- The graph of a linear equation is a straight line.

### Characteristics of \( Y = 2 | n - 3 | \):
- The presence of the absolute value \( | n - 3 | \) means that the function changes direction at \( n = 3 \), creating two linear segments: one for \( n < 3 \) and another for \( n \geq 3 \).
- Therefore, the graph of this function will have a "V" shape, indicating that it is not a straight line.

In summary, \( Y = 2 | n - 3 | \) is not a linear equation due to the absolute value component.