Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through \( (-4,-1) \) and \( (4,11) \) Type the point-slope form of the equation of the line. \( y+1=\frac{3}{2}(x+4) \) (Use integers or simplified fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. \( \square \) (Use integers or simplified fractions for any numbers in the equation.)

To find the slope-intercept form of the equation, we first need to calculate the slope (m) using the points given. The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - (-1)}{4 - (-4)} = \frac{12}{8} = \frac{3}{2} \] Now, using the point-slope form provided: \[ y + 1 = \frac{3}{2}(x + 4) \] To convert this into slope-intercept form (y = mx + b), we can expand and simplify: 1. Distribute \( \frac{3}{2} \): \[ y + 1 = \frac{3}{2}x + 6 \] 2. Subtract 1 from both sides: \[ y = \frac{3}{2}x + 5 \] So the slope-intercept form of the equation of the line is: \[ y = \frac{3}{2}x + 5 \]