Final answer:
The slope of the line passing through the points (10, 2) and (19, 14) is determined by calculating the difference in y-coordinates divided by the difference in x-coordinates, resulting in a slope of 4/3 or 1.333..., which rounds to 3/2.
Step-by-step explanation:
The slope of a line passing through two points can be found using the formula Δy/Δx, which represents the change in the y-coordinates divided by the change in the x-coordinates of the two points. The two points given are (10, 2) and (19, 14). To compute the slope, subtract the y-coordinate of the first point from the y-coordinate of the second point to find Δy, and subtract the x-coordinate of the first point from the x-coordinate of the second point to find Δx. So, Δy = 14 - 2 = 12 and Δx = 19 - 10 = 9, and the slope (m) is Δy/Δx = 12/9. Simplifying this, we get the slope as m = 4/3 or 1.333... . Thus, the correct answer is c) 3/2, which when converted to decimal form equals 1.5 and is the closest value to our calculated slope.