To find the equation of the line that passes through the points \((-20, 16)\) and \( (10, 4)\), we first need to determine the slope (m) of the line using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assign the points as follows:
- \( (x_1, y_1) = (-20, 16) \)
- \( (x_2, y_2) = (10, 4) \)
Now, substituting the values into the slope formula:
\[ m = \frac{4 - 16}{10 - (-20)} = \frac{-12}{10 + 20} = \frac{-12}{30} = -\frac{2}{5} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Substituting in \(m = -\frac{2}{5}\) and the point \((-20, 16)\):
\[ y - 16 = -\frac{2}{5}(x + 20) \]
Distributing the slope on the right-hand side:
\[ y - 16 = -\frac{2}{5}x - 8 \]
Now, adding 16 to both sides to isolate \(y\):
\[ y = -\frac{2}{5}x + 8 \]
To convert this to standard form \(Ax + By = C\), we can multiply through by 5 to eliminate the fraction:
\[ 5y = -2x + 40, \Rightarrow, 2x + 5y = 40 \]
Thus, the equation of the line in standard form is:
\[ 2x + 5y = 40 \]
So the correct answer from the options given is:
2x + 5y = 40.