1. The problem is to understand the concepts of linearity and continuity in graphs. 2. Linearity means the graph of a function is a straight line, which can be represented by the equation $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Continuity means the graph has no breaks, jumps, or holes; the function is continuous if for every point $x = a$, $$\lim_{x \to a} f(x) = f(a)$$. 4. For linear functions, continuity is always true because straight lines have no breaks. 5. To check linearity, verify if the function can be written in the form $$y = mx + b$$. 6. To check continuity, ensure the function's limit at every point equals the function's value at that point. 7. Example: The function $$y = 2x + 3$$ is linear and continuous. 8. The graph is a straight line with slope 2 and y-intercept 3. 9. Since it is a polynomial (degree 1), it is continuous everywhere. 10. Therefore, linearity implies continuity for such functions.