1. **State the problem:** Solve the linear equation $3x + 1 = -5$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Remember, whatever you do to one side of the equation, do to the other side. 3. **Step-by-step solution:** - Subtract 1 from both sides: $$3x + 1 - 1 = -5 - 1$$ $$3x = -6$$ - Divide both sides by 3: $$\frac{3x}{3} = \frac{-6}{3}$$ $$x = -2$$ 4. **Interpretation:** The solution $x = -2$ means that when $x$ is substituted back into the equation, the equality holds true. 5. **Additional information:** - The $x$-intercept of the line $y = 3x + 1$ is found by setting $y=0$: $$0 = 3x + 1 \Rightarrow 3x = -1 \Rightarrow x = -\frac{1}{3}$$ - The $y$-intercept is the value of $y$ when $x=0$: $$y = 3(0) + 1 = 1$$ 6. **Graph description:** The line has a positive slope of 3 and crosses the $y$-axis at 1. Among the given options, Graph C matches this description: a line with positive slope passing through the $y$-axis below the origin (at $y=1$).