\( \begin{array}{lll}\text { 8. }(3,0) ; m=-\frac{2}{3} & \text { 9. }(4,8) ; m=\frac{3}{4} & \text { 10. }(1,-3) ; m=4 \\ \text { 11. }(7,-5) ; m=-\frac{1}{7} & \text { 12. }(3,3) ; m=\frac{5}{3} & \text { 13. }(-1,-4) ; m=-2\end{array} \) WRITING AN EQUATION Write an equation in slope-intercept form of the line that passes through the given points. \( \begin{array}{lll}\text { 14. }(-1,-1),(1,5) & \text { 15. }(2,4),(3,6) & \text { 16. }(-2,3),(2,7) \\ \text { 17. }(4,1),(8,2) & \text { 18. }(-9,5),(-3,3) & \text { 19. }(1,2),(-2,-1)\end{array} \)

To write the equation of a line in slope-intercept form \(y = mx + b\), we need to determine the slope \(m\) and the y-intercept \(b\). The slope can be calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Once we have the slope, we can use one of the points to solve for \(b\) by substituting \(m\), \(x\), and \(y\) into the equation \(y = mx + b\). Let's solve each of the problems step by step. ### Problem 14: Points (-1, -1) and (1, 5) 1. **Calculate the slope \(m\)**: \[ m = \frac{5 - (-1)}{1 - (-1)} = \frac{5 + 1}{1 + 1} = \frac{6}{2} = 3 \] 2. **Use point (-1, -1) to find \(b\)**: \[ -1 = 3(-1) + b \implies -1 = -3 + b \implies b = 2 \] 3. **Equation**: \[ y = 3x + 2 \] ### Problem 15: Points (2, 4) and (3, 6) 1. **Calculate the slope \(m\)**: \[ m = \frac{6 - 4}{3 - 2} = \frac{2}{1} = 2 \] 2. **Use point (2, 4) to find \(b\)**: \[ 4 = 2(2) + b \implies 4 = 4 + b \implies b = 0 \] 3. **Equation**: \[ y = 2x + 0 \quad \text{or simply} \quad y = 2x \] ### Problem 16: Points (-2, 3) and (2, 7) 1. **Calculate the slope \(m\)**: \[ m = \frac{7 - 3}{2 - (-2)} = \frac{4}{4} = 1 \] 2. **Use point (-2, 3) to find \(b\)**: \[ 3 = 1(-2) + b \implies 3 = -2 + b \implies b = 5 \] 3. **Equation**: \[ y = 1x + 5 \quad \text{or simply} \quad y = x + 5 \] ### Problem 17: Points (4, 1) and (8, 2) 1. **Calculate the slope \(m\)**: \[ m = \frac{2 - 1}{8 - 4} = \frac{1}{4} \] 2. **Use point (4, 1) to find \(b\)**: \[ 1 = \frac{1}{4}(4) + b \implies 1 = 1 + b \implies b = 0 \] 3. **Equation**: \[ y = \frac{1}{4}x + 0 \quad \text{or simply} \quad y = \frac{1}{4}x \] ### Problem 18: Points (-9, 5) and (-3, 3) 1. **Calculate the slope \(m\)**: \[ m = \frac{3 - 5}{-3 - (-9)} = \frac{-2}{6} = -\frac{1}{3} \] 2. **Use point (-9, 5) to find \(b\)**: \[ 5 = -\frac{1}{3}(-9) + b \implies 5 = 3 + b \implies b = 2 \] 3. **Equation**: \[ y = -\frac{1}{3}x + 2 \] ### Problem 19: Points (1, 2) and (-2, -1) 1. **Calculate the slope \(m\)**: \[ m = \frac{-1 - 2}{-2 - 1} = \frac{-3}{-3} = 1 \] 2. **Use point (1, 2) to find \(b\)**: \[ 2 = 1(1) + b \implies 2 = 1 + b \implies b = 1 \] 3. **Equation**: \[ y = 1x + 1 \quad \text{or simply} \quad y = x + 1 \] ### Summary of Equations - **14**: \(y = 3x + 2\) - **15**: \(y = 2x\) - **16**: \(y = x + 5\) - **17**: \(y = \frac{1}{4}x\) - **18**: \(y = -\frac{1}{3}x + 2\) - **19**: \(y = x + 1\)