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 \( y=m x+b \).

Let the function be \( h(x) = x^{3} + 4 \). 1. **Evaluate the function at \( x=-3 \) and \( x=2 \):** \[ h(-3) = (-3)^3 + 4 = -27 + 4 = -23 \] \[ h(2) = (2)^3 + 4 = 8 + 4 = 12 \] 2. **Identify the points on the curve:** The two points are \( (-3, -23) \) and \( (2, 12) \). 3. **Calculate the slope \( m \) of the secant line:** \[ m = \frac{12 - (-23)}{2 - (-3)} = \frac{12 + 23}{2 + 3} = \frac{35}{5} = 7 \] 4. **Write the equation of the line in point-slope form:** Using the point \( (-3, -23) \), the equation is: \[ y - (-23) = 7\,(x - (-3)) \] \[ y + 23 = 7\,(x + 3) \] 5. **Convert to slope-intercept form \( y = mx + b \):** \[ y + 23 = 7x + 21 \] Subtract 23 from both sides: \[ y = 7x + 21 - 23 \] \[ y = 7x - 2 \] Thus, the equation of the secant line is: \[ y = 7x - 2 \]