Final answer:
The equation of the line with a slope of 3 and a y-intercept of 9 is y = 3x + 9. The 'm' in the equation represents the slope, with 'b' being the y-intercept, together defining the line's shape on a graph.
Step-by-step explanation:
To find the equation of a line that demonstrates direct variation and is a straight line through the origin, you would use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this instance, the line graph information provided tells us that the y-intercept is 9 and the slope (m) is 3. This means for every unit increase in x, y increases by 3. Therefore, the equation of this line is y = 3x + 9.
The m in the equation represents the slope, indicating how much the line moves up (positive slope) or down (negative slope) along the y-axis for each unit increment along the x-axis. The example provided clarifies how the slope (m) and y-intercept (b) determine the line's appearance on the graph.