To solve this problem, we're going to use the formula for finding the slope of a line that passes through two points (x₁, y₁) and (x₂, y₂), which is:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, our two points, (x₁, y₁) and (x₂, y₂), are (5,3) and (12,11) respectively.
We substitute these coordinates into our formula and perform the calculations:
Slope = (11 - 3) / (12 - 5)
= (8) / (7)
= 1.1428571428571428
So the slope of the line passing through the points (5, 3) and (12,11) is 1.1428571428571428.