1. **Problem Statement:** We need to 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 the slope and intercept:** Here, $m=3$ and $b=2$. 4. **Plotting points:** - When $x=0$, $y=3(0)+2=2$. - When $x=1$, $y=3(1)+2=5$. 5. **Graph characteristics:** Since the function is of the form $y=mx+b$, it is a linear function. 6. **Summary:** The graph is a straight line with slope 3 and y-intercept 2. **Final answer:** The function $y=3x+2$ is linear and its graph is a straight line with slope 3 and y-intercept 2.