Final answer:
The slope of the line passing through the points (1, -5) and (4, 1) is calculated as the change in y over the change in x, which results in a slope of 2.
Step-by-step explanation:
The slope of the line that goes through the points (1, -5) and (4, 1) is calculated using the formula for slope, which is (change in y) / (change in x). This is often referred to as 'rise over run'. To find the change in y, subtract the y-coordinate of the first point from the y-coordinate of the second point. Similarly, subtract the x-coordinate of the first point from the x-coordinate of the second point to find the change in x.
Change in y (rise)= 1 - (-5) = 1 + 5 = 6
Change in x (run)= 4 - 1 = 3
Therefore, the slope (m) is:
m = Change in y / Change in x = 6 / 3 = 2
The slope is 2, which means for every increase of 1 on the horizontal axis there is a rise of 2 on the vertical axis. This indicates a straight line with a positive slope.