1. **Problem Statement:** Sketch the graph of the function $y=3x+2$ and identify if it is linear. 2. **Formula and Explanation:** The function is given by $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m=3$ and $b=2$. 4. **Plot points:** - When $x=0$, $y=3(0)+2=2$ (y-intercept). - When $x=1$, $y=3(1)+2=5$. 5. **Draw the line:** Plot points $(0,2)$ and $(1,5)$ and draw a straight line through them. 6. **Check linearity:** Since the equation is in the form $y=mx+b$, it represents a linear function. **Final answer:** The graph of $y=3x+2$ is a straight line with slope 3 and y-intercept 2, so it is linear.