# FIND MISSING COORDINATE WHEN SLOPE IS GIVEN

Using any two points on the line, we can find slope of the line.

Let (x1, y1) and (x2, y2) be the two points on the line.

Slope (m) = (y2 - y1) / (x2 - x1)

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.

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