Determine the standard form of the equation of the line that passes through (-7, 8) and (0, 2). 

Solution:

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

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

Given that line passes through (-7, 8) and (0, 2) 

∴ Substituting (x₁, y₁) = (-7, 8) and (x₂, y₂) = (0, 2) in equation (1),

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

(y - 8) = [(2 - 8) / (0 - (-7)] [x - (-7)]

(y - 8) = (-6/ 7) (x + 7)

7y - 56 = -6x - 42

6x + 7y - 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 (-7, 8) and (0, 2). 

Summary:

The standard form of the equation of the line that passes through (-7, 8) and (0, 2) is 6x + 7y - 14 = 0.