Solve for the values of y given the values of x a) y = 1/3x -2. when x = -12 and x = 0 b) y = -x -4. when x = -4 and x = 4

Part A: Solve for y in the equation $y = \frac{1}{3}x - 2$

1. Break Down the Problem We need to evaluate the equation for two different values of $x$: $x = -12$ and $x = 0$.

2. Relevant Concepts For the equation $y = \frac{1}{3}x - 2$, we will substitute each value of $x$ into the equation.

3. Analysis and Detail

   • For $x = -12$: $y = \frac{1}{3}(-12) - 2$ $y = -4 - 2$ $y = -6$

   • For $x = 0$: $y = \frac{1}{3}(0) - 2$ $y = 0 - 2$ $y = -2$

4. Verify and Summarize We've calculated the values of $y$ for the given $x$ values.

Final Answer for Part A

• When $x = -12$, $y = -6$
• When $x = 0$, $y = -2$

Part B: Solve for y in the equation $y = -x - 4$

1. Break Down the Problem We need to evaluate the equation for two different values of $x$: $x = -4$ and $x = 4$.

2. Relevant Concepts For the equation $y = -x - 4$, we will substitute each value of $x$ into the equation.

3. Analysis and Detail

   • For $x = -4$: $y = -(-4) - 4$ $y = 4 - 4$ $y = 0$

   • For $x = 4$: $y = -(4) - 4$ $y = -4 - 4$ $y = -8$

4. Verify and Summarize We've calculated the values of $y$ for the given $x$ values.

Final Answer for Part B

• When $x = -4$, $y = 0$
• When $x = 4$, $y = -8$