Final answer:
To determine the value of r for a slope of −9/2 between points (-3,-4) and (-5,r), set up a proportion using the slope formula. Solve it by cross-multiplication to find that r equals 5.
Step-by-step explanation:
To find the value of r so that the line through (-3,-4) and (-5,r) has a slope of −9/2, we first need to recall that the slope formula is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of two distinct points on the line. Given that the slope is −9/2, we can set up a proportion using the coordinates of the points and the known slope:
(r - (-4)) / (-5 - (-3)) = −9/2
Find the difference in the y-coordinates:
r - (-4) = r + 4
Find the difference in the x-coordinates:
-5 - (-3) = -5 + 3 = -2
Now set up the proportion using the slope formula:
(r + 4) / (-2) = −9/2
Solving for r involves cross-multiplying the proportion:
-2 * r + 4 = −9/2 * -2
-2r - 8 = −18
-2r = −18 + 8
-2r = −10
r = −10 / -2
r = 5
Therefore, the value of r is 5 so that the line through the given points has the specified slope of −9/2.