How do you find the standard form of the equation of a line that goes through the points (0, 5) and (4, 0)?

To find the standard form of the equation of a line given two points, you can follow these steps:

1. Identify the Points: We have the points (0, 5) and (4, 0).
2. Calculate the Slope: The slope (m) of a line through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
   
   m = (y₂ – y₁) / (x₂ – x₁)
   
   
   Substituting the points:
   
   
   m = (0 – 5) / (4 – 0) = -5 / 4
   
3. Use the Point-Slope Form: Now you can use the point-slope form of a line, which is given by the equation:
   
   
   y – y₁ = m(x – x₁)
   
   
   Using point (0, 5):
   
   
   y – 5 = -5/4(x – 0)
   
4. Simplify to Slope-Intercept Form: Distributing the slope:
   
   
   y – 5 = -5/4x
   
   
   y = -5/4x + 5
   
5. Convert to Standard Form: The standard form of the equation of a line is typically written as Ax + By = C. We can rearrange the equation:
   
   
   5/4x + y = 5
   
   
   To eliminate the fraction, multiply the entire equation by 4:
   
   
   5x + 4y = 20
   

So, the standard form of the equation of the line that passes through the points (0, 5) and (4, 0) is:

5x + 4y = 20