To find the equation of the line passing through the points \((44, 6)\) and \((-4, -6)\), we can start by calculating the slope \(m\) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (44, 6)\) and \((x_2, y_2) = (-4, -6)\). Substituting these values into the slope formula gives:
\[ m = \frac{-6 - 6}{-4 - 44} = \frac{-12}{-48} = \frac{1}{4} \]
Now that we have the slope, we can use point-slope form to write the equation of the line. The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
Using point \((44, 6)\) and the slope \(m = \frac{1}{4}\):
\[ y - 6 = \frac{1}{4}(x - 44) \]
Now we can simplify this equation:
\[ y - 6 = \frac{1}{4}x - \frac{44}{4} \]
\[ y - 6 = \frac{1}{4}x - 11 \]
Adding \(6\) to both sides:
\[ y = \frac{1}{4}x - 11 + 6 \]
\[ y = \frac{1}{4}x - 5 \]
Thus, the equation of the line passing through the points \((44, 6)\) and \((-4, -6)\) is:
\[ y = \frac{1}{4}x - 5 \]