Wring the equation of a secant line Given \( h(x)=x^{3}+4 \), find the equation of the secant line passing through \( (-3, h(-3)) \) and \( (2, h(2)) \). Write your answer in the form \( y=m x+b \).

To find the equation of the secant line, we first need to calculate the values of \( h(-3) \) and \( h(2) \). Calculating \( h(-3) \): \[ h(-3) = (-3)^3 + 4 = -27 + 4 = -23 \] So the first point is \( (-3, -23) \). Calculating \( h(2) \): \[ h(2) = (2)^3 + 4 = 8 + 4 = 12 \] So the second point is \( (2, 12) \). Now, we can find the slope \( m \) of the secant line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - (-23)}{2 - (-3)} = \frac{12 + 23}{2 + 3} = \frac{35}{5} = 7 \] Now we have the slope \( m = 7 \). Using point-slope form \( y - y_1 = m(x - x_1) \) with one of the points, say \( (2, 12) \): \[ y - 12 = 7(x - 2) \] Expanding this gives: \[ y - 12 = 7x - 14 \] \[ y = 7x - 2 \] Therefore, the equation of the secant line is: \[ y = 7x - 2 \]