write an equation for (-6,5),(5,0),(5,6)

Question

write an equation for these points (-6,5),(5,0),(5,6).

Answer 1

The points are (-6, 5), (5, 0) and (5, 6).

1. Plot these points on a rectangular coordinate system. There is no possible to all points are lie on the same line.

2. So, connect every two points with a smooth line. There are three lines are available.

Let the points are A = (-6, 5), B = (5, 0) and C = (5, 6).

Find the equation of line AB :

The points are A = (x₁, y₁) = (-6, 5) and B = (x₂, y₂) = (5, 0).

Slope m = [y₂ - y₁] / [x₂ - x₁] = [0 - 5] / [5 - (-6)] = - 5/11.

The point - slope form of line equation : y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point.

m = - 5/11 and (x₁, y₁) =  (-6, 5)

y - 5 = - 5/11 [x - (-6)]

11(y - 5) = - 5(x + 6)

11y - 55 = - 5x - 30

5x + 11y - 25 = 0

Find the equation of line BC :

The points are B = (x₁, y₁) = (5, 0) and C = (x₂, y₂) = (5, 6).

Slope m = [y₂ - y₁] / [x₂ - x₁] = [6 - 0] / [5 - 0] = 6/0.

m = 6/0 and (x₁, y₁) =  (5, 0)

The point - slope form of line equation : y - y₁ = m(x - x₁).

y - 0 = 6/0 [x - 5]

0(y - 0) = 6[x - 5]

0 = 6x - 30

6x - 30 = 0.

Find the equation of line CA :

The points are C = (x₁, y₁) = (5, 6) and A = (x₂, y₂) = (-6, 5).

Slope m = [y₂ - y₁] / [x₂ - x₁] = [5 - 6] / [- 6 - 5] = 1/11.

m = 1/11 and (x₁, y₁) =  (5, 6)

The point - slope form of line equation : y - y₁ = m(x - x₁).

y - 6 = 1/11 [x - 5]

11(y - 6) = 1[x - 5]

11y - 66 = x - 5

x - 11y + 61 = 0.