Final answer:
The slope of the line passing through the points (1,1) and (10,7) is calculated as the change in y divided by the change in x, which gives us a slope of 2/3.
Step-by-step explanation:
The slope of a line that goes through two points can be found using the slope formula, which is (change in y) / (change in x). Here, let's calculate the slope of the line that passes through the points (1,1) and (10,7).
To find the change in y, subtract the y-value of the first point from the y-value of the second point: 7 - 1 = 6. To find the change in x, subtract the x-value of the first point from the x-value of the second point: 10 - 1 = 9.
Now divide the change in y by the change in x to get the slope: 6 / 9 = 2/3. Therefore, the slope of the line is 2/3, which means the line rises 2 units for every 3 units it runs horizontally.