1. The problem is to graph the linear equation $y = 3x - 4$. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. For $y = 3x - 4$, the slope $m = 3$ and the y-intercept $b = -4$. 4. The y-intercept is the point where the line crosses the y-axis, which is at $(0, -4)$. 5. To find the x-intercept, set $y = 0$ and solve for $x$: $$0 = 3x - 4$$ $$3x = 4$$ $$x = \frac{4}{3}$$ 6. The x-intercept is at $\left(\frac{4}{3}, 0\right)$. 7. Using the slope $3$, which means rise over run is $3/1$, from the y-intercept $(0, -4)$, move up 3 units and right 1 unit to plot another point at $(1, -1)$. 8. Connect the points $(0, -4)$ and $(1, -1)$ with a straight line to graph the equation. Final answer: The line passes through points $(0, -4)$ and $(1, -1)$ with slope 3.