Determine the slope of a line passing through each pair of points. \( \begin{array}{ll}\text { 3. }(0,0) \text { and }(6,3) & \text { 4. }(2,1) \text { and }(-8,5) \\ \text { 5. }(-2,-3) \text { and }(-3,1) & \text { 6. }(-5,2) \text { and }(3,2)\end{array} \)

To determine the slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's apply this formula to each pair of points: --- **3. Points \((0, 0)\) and \((6, 3)\)** \[ m = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \] **Slope:** \( \frac{1}{2} \) --- **4. Points \((2, 1)\) and \((-8, 5)\)** \[ m = \frac{5 - 1}{-8 - 2} = \frac{4}{-10} = -\frac{2}{5} \] **Slope:** \( -\frac{2}{5} \) --- **5. Points \((-2, -3)\) and \((-3, 1)\)** \[ m = \frac{1 - (-3)}{-3 - (-2)} = \frac{4}{-1} = -4 \] **Slope:** \( -4 \) --- **6. Points \((-5, 2)\) and \((3, 2)\)** \[ m = \frac{2 - 2}{3 - (-5)} = \frac{0}{8} = 0 \] **Slope:** \( 0 \) --- **Summary of Slopes:** 1. **Problem 3:** \( \frac{1}{2} \) 2. **Problem 4:** \( -\frac{2}{5} \) 3. **Problem 5:** \( -4 \) 4. **Problem 6:** \( 0 \)