Find the point-slope equation for the line that passes through the points \( (2,1) \) and \( (-2,5) \). Use the first point in your equation. \( y-[?]=[\square(x-[\square) \)

To find the point-slope equation of the line, we first need to calculate the slope \( m \) using the two points \( (2,1) \) and \( (-2,5) \). The formula for slope \( m \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 1}{-2 - 2} = \frac{4}{-4} = -1. \] Now that we have the slope, we can use the point-slope form \( y - y_1 = m(x - x_1) \). With \( (x_1, y_1) = (2, 1) \) and \( m = -1 \), we can plug these values into the equation: \[ y - 1 = -1(x - 2). \] So, the complete point-slope equation is: \[ y - 1 = -1(x - 2). \]