Final answer:
The value of r for the line to have a slope of -9/2, we set up a slope proportion and solve it to find that r equals -13.
Step-by-step explanation:
To find the value of r so that the line through the points (-3,-4) and (-5,r) has a slope of −9/2, we can set up a proportion using the slope formula:
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the known values, we get:
(r - (-4)) / (-5 - (-3)) = -9/2
This simplifies to:
(r + 4) / (-2) = -9/2
By cross-multiplying, we obtain:
2(r + 4) = 9(−2)
Which simplifies to:
2r + 8 = -18
Subtracting 8 from both sides, we get:
2r = -26
Dividing by 2, we find:
r = -13
Therefore, the value of r is −13.