Final answer:
The equation of the line with a slope of 3 and y-intercept of 9 is y = 3x + 9. The slope-intercept form is used to define the steepness and the crossing point of the line on the y-axis.
Step-by-step explanation:
The student was asked to write the slope-intercept form of the equation for the line. To answer this question, we need to understand the definitions of slope and y-intercept in the context of a linear equation. The slope-intercept form of a linear equation is typically written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents the steepness of the line, and the y-intercept represents the point where the line crosses the y-axis.
Based on the information provided, the y-intercept is 9, and the slope of the line is 3. Therefore, the equation of the line that has a slope of 3 and a y-intercept of 9 is y = 3x + 9. This example illustrates how the slope and y-intercept determine the shape and position of the line on a graph.