Find the slope of the line that passes through each pair of points. \( \begin{array}{llll}5 .(4,3) \text { and }(-6,-5) & \text { 6. }(12,-2) \text { and }(4,8) & 7 .(-8,7) \text { and }(-8,12) & 8 .(-2,-5) \text { and }(7,-5)\end{array} \)

To find the slope of the line that passes through each pair of points, we can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Let's calculate the slope for each pair of points step by step. ### 1. Points: \( (4, 3) \) and \( (-6, -5) \) - \(x_1 = 4\), \(y_1 = 3\) - \(x_2 = -6\), \(y_2 = -5\) Calculating the slope: \[ m = \frac{-5 - 3}{-6 - 4} = \frac{-8}{-10} = \frac{4}{5} \] ### 2. Points: \( (12, -2) \) and \( (4, 8) \) - \(x_1 = 12\), \(y_1 = -2\) - \(x_2 = 4\), \(y_2 = 8\) Calculating the slope: \[ m = \frac{8 - (-2)}{4 - 12} = \frac{10}{-8} = -\frac{5}{4} \] ### 3. Points: \( (-8, 7) \) and \( (-8, 12) \) - \(x_1 = -8\), \(y_1 = 7\) - \(x_2 = -8\), \(y_2 = 12\) Calculating the slope: Since both points have the same \(x\)-coordinate, the slope is undefined (vertical line). ### 4. Points: \( (-2, -5) \) and \( (7, -5) \) - \(x_1 = -2\), \(y_1 = -5\) - \(x_2 = 7\), \(y_2 = -5\) Calculating the slope: Since both points have the same \(y\)-coordinate, the slope is \(0\) (horizontal line). ### Summary of Slopes 1. Slope between \( (4, 3) \) and \( (-6, -5) \): \( \frac{4}{5} \) 2. Slope between \( (12, -2) \) and \( (4, 8) \): \( -\frac{5}{4} \) 3. Slope between \( (-8, 7) \) and \( (-8, 12) \): Undefined 4. Slope between \( (-2, -5) \) and \( (7, -5) \): \( 0 \)