Complete the equation of the line through \( (6,-6) \) and \( (8,8) \). Use exact numbers. \( y=\square \)

To find the equation of the line passing through the points \( (6, -6) \) and \( (8, 8) \), we'll follow these steps: 1. **Calculate the slope (\( m \))**: The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the given points: \[ m = \frac{8 - (-6)}{8 - 6} = \frac{14}{2} = 7 \] 2. **Use the slope-intercept form (\( y = mx + b \))** to find the y-intercept (\( b \)): We can use either of the two points to solve for \( b \). Let's use \( (6, -6) \): \[ -6 = 7(6) + b \\ -6 = 42 + b \\ b = -6 - 42 \\ b = -48 \] 3. **Write the equation of the line**: Substituting the slope and y-intercept back into the slope-intercept form: \[ y = 7x - 48 \] **Final Answer:** \[ y = 7x - 48 \]