Question

Find the value of "r" so the line that passes through each pair of points has the given slope.

Given Points: (5, -3) and (r, -5), with a slope of m = 2.
Find the value of "r" so the line that passes through each pair of points has the given slope.
Given Points: (6, r) and (-4, 9), with a slope of m = 3/2.

Answer 1

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.