Determine the standard form of the equation of the line that passes through (6,0) and (2,-7).

Solution:

The standard equation of a straight line is Ax + By + C = 0.

Equation of the line is (y - y₁) = [(y₂ - y₁) / (x₂ - x₁)] (x - x₁) ------(1)

Given that line passes through (6, 0) and (2, -7) 

∴ Substituting (x₁, y₁) = (6, 0) and (x₂, y₂) = (2,-7) in equation (1),

(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)] (x - x₁)

(y - 0) = [(-7 - 0)/ (2 - 6)] (x - 2)

y = (-7 / -4) (x - 2)

4y = 7x - 14

7x - 4y - 14 = 0

This is the required equation of the line which is in the general form.

Determine the standard form of the equation of the line that passes through (6,0) and (2,-7).

Summary:

The standard form of the equation of the line that passes through (6,0) and (2,-7) is 7x - 4y - 14 = 0.