Final answer:
The slope of a line passing through the points (-4,3) and (-4,-7) is undefined because it's a vertical line, and the x-values are the same, which would lead to division by zero.
Step-by-step explanation:
When you're asked to find the slope of a line that passes through two points, you're looking for the rate at which the y-value changes for each unit change in the x-value. However, in the case of the points (-4,3) and (-4,-7), you may notice that the x-value does not change, which means that the line is vertical. A vertical line does not have a defined slope; therefore, the slope is considered to be undefined or infinite.
In more general cases, to calculate the slope given two points, you would use the formula m = (Y2 - Y1) / (X2 - X1), where m represents the slope, (X1, Y1) is the first point, and (X2, Y2) is the second point. However, if X1 equals X2, this would result in a division by zero, which is not possible in mathematics.