1. **State the problem:** We are given the linear function $y = 3x - 2$ and asked to understand its properties and graph. 2. **Formula and rules:** The equation $y = mx + b$ represents a straight line where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = 3$ and $b = -2$. This means the line rises 3 units vertically for every 1 unit it moves horizontally. 4. **Find the y-intercept:** When $x=0$, $y = 3(0) - 2 = -2$. So the line crosses the y-axis at $(0, -2)$. 5. **Find the x-intercept:** Set $y=0$ and solve for $x$: $$0 = 3x - 2$$ $$3x = 2$$ $$x = \frac{2}{3}$$ 6. **Plot points:** The line passes through $(0, -2)$ and $(\frac{2}{3}, 0)$. 7. **Explain the graph:** The line extends infinitely in both directions with slope 3, crossing the y-axis at -2 and x-axis at $\frac{2}{3}$. **Final answer:** The line $y = 3x - 2$ has slope 3, y-intercept -2, and x-intercept $\frac{2}{3}$.