Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9). 

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 (-5, 0) and (0, -9) 

∴ Substituting (x₁, y₁) = (-5, 0) and (x₂, y₂) = (0, -9) in equation (1),

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

(y - 0) = [(-9 - 0) / (0 - (-5)] [x -(-5)]

y = (-9 / 5) (x + 5)

5y = -9x - 45

9x + 4y + 45 = 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 (-5,0) and (0,-9). 

Summary:

The standard form of the equation of the line that passes through (-5,0) and (0,-9) is 9x + 4y + 45 = 0.