To find the equation of the line that passes through the points \((7, 4)\) and \((5, -4)\), we can use the two-point form of the equation of a line.
-
Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we can take \((x_1, y_1) = (7, 4)\) and \((x_2, y_2) = (5, -4)\): \[ m = \frac{-4 - 4}{5 - 7} = \frac{-8}{-2} = 4 \]
-
Use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Plugging in one of the points, say \((7, 4)\): \[ y - 4 = 4(x - 7) \]
-
Expand and simplify: \[ y - 4 = 4x - 28 \] \[ y = 4x - 28 + 4 \] \[ y = 4x - 24 \]
So the equation of the line that passes through the points \((7, 4)\) and \((5, -4)\) is:
\[ y = 4x - 24 \]
Therefore, the correct answer is:
y = 4x - 24.