Final answer:
To find the value of r, we can use the formula for slope and solve for r. For the first pair of points, the value of r is 4. For the second pair of points, the value of r is 24.
Step-by-step explanation:
To find the value of r so the line that passes through each pair of points has the given slope, we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
For the first pair of points, (5, -3) and (r, -5), with a slope of 2, we can plug in the values:
2 = (-5 - (-3)) / (r - 5)
Simplifying the equation:
2 = -2 / (r - 5)
Multiplying both sides by (r - 5) to isolate r:
2(r - 5) = -2
r - 5 = -1
r = 4
Therefore, the value of r is 4.
For the second pair of points, (6, r) and (-4, 9), with a slope of 3/2, we can use the same formula:
3/2 = (9 - r) / (-4 - 6)
Simplifying the equation:
3/2 = (9 - r) / -10
Multiplying both sides by -10 to isolate r:
3(-10) = 2(9 - r)
-30 = 18 - 2r
-2r = -48
r = 24
Therefore, the value of r is 24.