Final answer:
The equation of the line with points (15, 3) and (0, 0) is y = 1/5x. This is derived by finding the slope, which is positive, indicating that the line slopes upward. None of the provided options exactly matches the calculated equation.
The correct option is not given.
Step-by-step explanation:
The question asks for the equation of a line given two points: (15, 3) and (0, 0). To find the equation of a line, we need the slope (m) and y-intercept (b).
The slope, m, is calculated by the change in y divided by the change in x (rise over run). For our points, m = (3 - 0) / (15 - 0) = 3/15 = 1/5.
Thus, the slope is positive, indicating the line slopes upward to the right. Since one point is (0, 0), which is the origin, the y-intercept b is also 0. Therefore, the equation is y = 1/5x + 0, which simplifies to y = 1/5x.
This corresponds to option b: y = 1/5x + 3; however, the constant term according to the given points should be 0, not 3, so none of the provided options perfectly matches the calculated equation.
Additional reference is made to the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In the case of the line with slope 3 and y-intercept 9, y = 9 + 3x as illustrated in the provided figures and tables. Note that for a line with slope b > 0, the line slopes upward, and if b < 0, the line slopes downward.
The correct option is not given.