Find the Linear Function with Slope ±2 and Domain x > 3

The following is a function that is positive in domain:

$3 < x$

Choose the equation that describes it given that the absolute value of the slope is 2.

To address this problem, we follow these steps:

• Step 1: A linear function in slope-intercept form is $y = mx + c$. Given slope $|m| = 2$, possible equations are $y = 2x + c$ and $y = -2x + c$.
• Step 2: Consider positivity for $x > 3$ condition.
  - For $y = 2x + c$ : We need $y = 2x + c > 0$. Solving yields $2x > -c$, meaning the function is positive when $x > \frac{-c}{2}$.
  - For $y = -2x + c$: Similarly, $-2x + c > 0$ provides $c > 2x$ or $x < \frac{c}{2}$, implying negativity above $x = \frac{c}{2}$.
• Step 3: Examine behavior at $x = 3$:
  - For $y = 2x + c$, it should be $2(3) + c > 0$; simplifying: $6 + c > 0 \rightarrow c > -6$.
  - For $y = -2x + c$, since positive domain minimum is $x > 3$, it’s negative $x > \frac{c}{2}$.
• Step 4: Confirms the correct function must work for any $c > -6$, resultant choice: $y = 2x - 6$. It remains positive as x increases past 3.

Thus, the correct equation satisfies all parameters: $y = 2x - 6$.