The function y = 9 + 3x is a linear equation because it follows the format y = mx + b, with m representing the constant slope and b representing the y-intercept. By plotting various x values, it's shown that the rate of change is constant, forming a straight line on a graph.
The function provided in the question appears to have a typo, but interpreting the question, we are asked if the equation y = 9 + 3x is linear or nonlinear. This is indeed a linear equation, as it is of the form y = mx + b, where m is the slope and b is the y-intercept. In this equation, the slope (m) is 3, which means with every increase of 1 in x, y increases by 3. The y-intercept (b) is 9, which is the point where the line crosses the y-axis. To visualize this, by plotting different values of x and calculating the corresponding y values, a line can be drawn to show a constant rate of change, which defines a linear relationship. Figure A1 demonstrates how these points, when plotted on a graph, form a straight line, confirming its linearity.