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. (Use integers or simplified fractions for any numbers in the equation.)

To find the equation of the line, we first need to calculate the slope (m) using the two given points \( (-4,-1) \) and \( (4,11) \). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - (-1)}{4 - (-4)} = \frac{12}{8} = \frac{3}{2} \] Now, using the point-slope form \( y - y_1 = m(x - x_1) \) with one of the points, say \( (-4, -1) \): \[ y - (-1) = \frac{3}{2}(x - (-4)) \] This simplifies to: \[ y + 1 = \frac{3}{2}(x + 4) \] Now, in slope-intercept form \( y = mx + b \), we can distribute and simplify further: \[ y + 1 = \frac{3}{2}x + 6 \] \[ y = \frac{3}{2}x + 5 \] The point-slope form of the equation is \( y + 1 = \frac{3}{2}(x + 4) \) and the slope-intercept form is \( y = \frac{3}{2}x + 5 \).