FIND MISSING COORDINATE WHEN SLOPE IS GIVEN

Find the value of x and y so that the line through the pair of points has the given slope.

Problem 1 :

(x, 3) and (5, 9) and slope (m) = 2

Solution :

Let (x₁, y₁) ==> (x, 3) and (x₂, y₂) ==> (5, 9)

m = (9 - 3) / (5 - x)

By applying the value of m, we get

2 = 6/(5 - x)

Doing cross multiplication, we get

5 - x = 12

Subtracting 5 on both sides, we get

-x = 12 - 5

-x = 7

x = -7

So, the value of x is -7.

Problem 2 :

(-2, 3) and (4, y) and slope (m) = -3

Solution :

Let (x₁, y₁) ==> (-2, 3) and (x₂, y₂) ==> (4, y)

m = (y - 3) / (4 - (-2))

m = (y - 3) / 6

By applying the value of m, we get

-3 = (y - 3) / 6

Doing cross multiplication, we get

y - 3 = -3(6)

y - 3 = -18

Add 3 on both sides, we get

y = -18 + 3

y = -15

So, the value of y is -15.

Problem 3 :

(-3, -5) and (4, y) and slope (m) = 3

Solution :

Let (x₁, y₁) ==> (-3, -5) and (x₂, y₂) ==> (4, y)

m = (y - (-5)) / (4 - (-3))

m = (y + 5) / 7

By applying the value of m, we get

3 = (y + 5) / 7

Doing cross multiplication, we get

y + 5 = 3(7)

y + 5 = 21

Subtract 5 on both sides, we get

y = 21 - 5

y = 16

So, the value of y is 16.

Problem 4 :

(-8, -2) and (x, 2) and slope (m) = 1/2

Solution :

Let (x₁, y₁) ==> (-8, -2) and (x₂, y₂) ==> (x, 2)

m = (2 - (-2)) / (x - (-8))

m = 4 / (x + 8)

By applying the value of m, we get

1/2 = 4 / (x + 8)

Doing cross multiplication, we get

x + 8 = 4(2)

x + 8 = 8

Subtracting 8 on both sides. We get

x = 8 - 8

x = 0

So, the value of x is 0.