How do i solve the equation (-7,1),(7,8)?

Question

How do I solve the equation?

Answer 1

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the points are (x₁, y₁) = (- 7, 1) and (x₂, y₂) = (7, 8).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(8 - 1)/(7 - (-7))]

m  = [7/14]

⇒ m = 1/2.

Now, the line equation is y = (1/2)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (- 7, 1).

1 = (1/2)(- 7) + b

b = 1 + (7/2)

b = (2 + 7)/2

⇒ b = 9/2.

The line equation in slope - intercept - form is y = (1/2)x + (9/2).

Subtract y from each side.

x/2 - y = - 9/2

(x - 2y)/2 = - 9/2

 The standard form the equation of the line is x - 2y = - 9.