15 passes through \( (4,-4) \) and \( (8,-10) \)

To find the equation of the line that passes through the points \( (4, -4) \) and \( (8, -10) \), we can follow these steps: 1. **Calculate the slope (m)** of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (4, -4) \) and \( (x_2, y_2) = (8, -10) \). 2. **Use the point-slope form** of the equation of a line: \[ y - y_1 = m(x - x_1) \] We can use either of the two points for \( (x_1, y_1) \). Let's calculate the slope first. Using the coordinates: - \( x_1 = 4 \) - \( y_1 = -4 \) - \( x_2 = 8 \) - \( y_2 = -10 \) Now, we can calculate the slope \( m \). \[ m = \frac{-10 - (-4)}{8 - 4} = \frac{-10 + 4}{4} = \frac{-6}{4} = -\frac{3}{2} \] Now that we have the slope, we can use the point-slope form with point \( (4, -4) \): \[ y - (-4) = -\frac{3}{2}(x - 4) \] This simplifies to: \[ y + 4 = -\frac{3}{2}(x - 4) \] Now, let's distribute and simplify: \[ y + 4 = -\frac{3}{2}x + 6 \] Subtracting 4 from both sides gives: \[ y = -\frac{3}{2}x + 2 \] Thus, the equation of the line that passes through the points \( (4, -4) \) and \( (8, -10) \) is: \[ y = -\frac{3}{2}x + 2 \]