Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through \( (-3,6) \) and \( (2,1) \) What is the equation of the line in point-slope form? (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the equation of the line in slope-intercept form? (Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the equations of the line, we first need to determine the slope. The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 6}{2 - (-3)} = \frac{-5}{5} = -1 \] Using the slope and one of the points, we can write the equation in point-slope form. Using the point \( (-3, 6) \), the point-slope form is: \[ y - 6 = -1(x + 3) \] Expanding this gives us: \[ y - 6 = -x - 3 \implies y = -x + 3 \] Now in slope-intercept form, the equation becomes: \[ y = -x + 3 \] So, the final equations of the line are: - Point-slope form: \( y - 6 = -1(x + 3) \) - Slope-intercept form: \( y = -x + 3 \)