WRITING AN EQUATION Write an equation in point-slope form of the line that passes through the given point and has the given slope. \( \begin{array}{lll}\text { 8. }(3,0) ; m=-\frac{2}{3} & \text { 9. }(4,8) ; m=\frac{3}{4} & \text { 10. }(1,-3) ; m=4 \\ \text { 11. }(7,-5) ; m=-\frac{1}{7} & \text { 12. }(3,3) ; m=\frac{5}{3} & \text { 13. }(-1,-4) ; m=\end{array} \)

Sure! The **point-slope form** of a line is given by: \[ y - y_1 = m(x - x_1) \] where \((x_1, y_1)\) is a point on the line and \(m\) is the slope. Let's apply this to each of the given problems: --- ### **Problem 8** **Given:** Point \((3, 0)\) and slope \(m = -\frac{2}{3}\) **Equation:** \[ y - 0 = -\frac{2}{3}(x - 3) \] \[ \boxed{y = -\frac{2}{3}(x - 3)} \] --- ### **Problem 9** **Given:** Point \((4, 8)\) and slope \(m = \frac{3}{4}\) **Equation:** \[ y - 8 = \frac{3}{4}(x - 4) \] \[ \boxed{y - 8 = \frac{3}{4}(x - 4)} \] --- ### **Problem 10** **Given:** Point \((1, -3)\) and slope \(m = 4\) **Equation:** \[ y - (-3) = 4(x - 1) \] \[ y + 3 = 4(x - 1) \] \[ \boxed{y + 3 = 4(x - 1)} \] --- ### **Problem 11** **Given:** Point \((7, -5)\) and slope \(m = -\frac{1}{7}\) **Equation:** \[ y - (-5) = -\frac{1}{7}(x - 7) \] \[ y + 5 = -\frac{1}{7}(x - 7) \] \[ \boxed{y + 5 = -\frac{1}{7}(x - 7)} \] --- ### **Problem 12** **Given:** Point \((3, 3)\) and slope \(m = \frac{5}{3}\) **Equation:** \[ y - 3 = \frac{5}{3}(x - 3) \] \[ \boxed{y - 3 = \frac{5}{3}(x - 3)} \] --- ### **Problem 13** **Given:** Point \((-1, -4)\) and slope \(m = \) *[Slope not provided]* It seems the slope \(m\) for Problem 13 is missing. If you provide the slope, I can help you form the corresponding point-slope equation. --- Feel free to ask if you need further assistance with any of these problems!