Determine the standard form of the equation of the line that passes through (0, 5) and (4,0).

Solution:

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

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

Given that line passes through (0, 5) and (4, 0) 

∴ Substituting (x₁, y₁) = (0, 5) and (x₂, y₂) = (4, 0) in equation (1),

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

(y - 5) = [(0 - 5)/ (4 - 0)] [x - 0]

(y - 5) = (-5 / 4) x

4y - 20 = -5x 

5x + 4y - 20 = 0

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

Determine the standard form of the equation of the line that passes through (0, 5) and (4,0).

Summary:

The standard form of the equation of the line that passes through (0, 5) and (4,0) is 5x + 4y - 20 = 0.