Final answer:
To find the equation of the tangent line to the graph of f(x) at the point (5,9), we use the constant slope of the function which is 3, resulting in the equation y = 3x + 6 for the tangent line.
Step-by-step explanation:
To find an equation of the line tangent to the graph of f(x) at the point (5,9), we need to determine the slope of f(x). Since the equation y = 9 + 3x represents this function, its slope, or m term, is 3. This is confirmed by Figure A1, showing that for every increase of 1 on the horizontal axis, there is a rise of 3 on the vertical axis.
Because the slope of f(x) is constant along the entire line, the slope at the point (5,9) is also 3. Therefore, the tangent line at this point will have the same slope of 3. Using the point-slope form of a line, we get the equation y - 9 = 3(x - 5), which simplifies to y = 3x + 6.