Determine the Standard Form of the Equation of the Line That Passes Through (0, 5) and (40, 0)

To find the standard form of the equation of a line given two points, we can use the two-point form of the line equation. The two points we have are (0, 5) and (40, 0).

First, we need to calculate the slope (m) of the line using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

Here, (x₁, y₁) = (0, 5) and (x₂, y₂) = (40, 0).

Substituting the values in, we have:

m = (0 – 5) / (40 – 0) = -5 / 40 = -1/8

Now that we have the slope, we can use the point-slope form of the equation of a line:

y – y₁ = m(x – x₁)

Using point (0, 5):

y – 5 = -1/8(x – 0)

This simplifies to:

y – 5 = -1/8x

Now, we need to rearrange this into standard form (Ax + By = C). First, add 5 to both sides:

y = -1/8x + 5

Next, we’ll eliminate the fraction by multiplying through by 8:

8y = -x + 40

Rearranging this gives:

x + 8y = 40

So, the standard form of the equation of the line that passes through the points (0, 5) and (40, 0) is:

x + 8y = 40