Final answer:
To determine the value of r for the points (4,r) and (r,2) to have a slope of -5/3, the formula for the slope is applied to set up the equation and solve for r, resulting in r being 7.
Step-by-step explanation:
Using the formula for the slope of a line between two points (x1, y1) and (x2, y2), which is (y2 - y1) / (x2 - x1).
Applying this to our points:
m = (2 - r) / (r - 4)
Since we are given that the slope m is -5/3, we can set up an equation:
-5/3 = (2 - r) / (r - 4)
Cross-multiplying to solve for r gives us:
-5(r - 4) = 3(2 - r)
-5r + 20 = 6 - 3r
Combining like terms and solving for r:
-2r = -14
r = 7
Therefore, the value of r that makes the slope -5/3 is 7.