Final answer:
Mary received conflicting information because the actual slope of the line through the points (1, 3) and (6, -2) is -1, not 3. If the slope is 3 and we use the point (1, 3), the equation of the line is y = 3x. However, if the points are correct, the slope is -1 and the equation is y = -x + 4.
Step-by-step explanation:
Mary was given incorrect information because the slope of a line through points (1, 3) and (6, -2) cannot be 3. To verify, we calculate the actual slope using the formula slope (m) = (change in y) / (change in x). Here, the change in y is -2 - 3, and the change in x is 6 - 1, which results in a slope of -5/5 or -1, not 3.
If the slope is indeed 3 and the point (1, 3) is on the line, then using the point-slope equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, an equation for the line would be y - 3 = 3(x - 1). This simplifies to y = 3x, since the y-intercept (b) is 0. Therefore, another point on this line could be (2, 6), where x = 2 and y = 3(2) = 6.
If the given points are correct, we already calculated the slope as -1. The equation of the line using the point-slope form with point (1, 3) would be y - 3 = -1(x - 1), simplified to y = -x + 4. Hence, this line intersects the y-axis at 4, so the y-intercept is 4.