Final answer:
The correct slope-intercept form equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept, the point where the line crosses the y-axis.
Step-by-step explanation:
The student is asking for the correct form of the slope-intercept equation of a line. This form is represented by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope signifies the steepness of the line, and it is calculated as the rise over the run. The y-intercept is the point where the line crosses the y-axis, and it can be represented as the point (0, b).
Through the provided example, we see that a line with a slope of 3 and y-intercept of 9 would have a rise of 3 units on the vertical axis for every 1 unit increase on the horizontal axis. The line equation that represents these characteristics is y = 3x + 9.
Of the options given to the student, the correct slope-intercept form is thus:
a) y = mx + b.