Writing the equation of a line through two given points Find an equation for the line that passes through the points \( (-4,-1) \) and \( (6,-5) \).

To find the equation of the line that passes through the points \((-4, -1)\) and \((6, -5)\), we can follow these steps: 1. **Calculate the slope (m)** of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (-4, -1)\) and \((x_2, y_2) = (6, -5)\). Substituting the values: \[ m = \frac{-5 - (-1)}{6 - (-4)} = \frac{-5 + 1}{6 + 4} = \frac{-4}{10} = -\frac{2}{5} \] 2. **Use the point-slope form** of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] We can use either of the two points. Let's use the point \((-4, -1)\). Substituting \(m = -\frac{2}{5}\), \(x_1 = -4\), and \(y_1 = -1\): \[ y - (-1) = -\frac{2}{5}(x - (-4)) \] Simplifying this: \[ y + 1 = -\frac{2}{5}(x + 4) \] 3. **Distribute the slope**: \[ y + 1 = -\frac{2}{5}x - \frac{2}{5} \cdot 4 \] \[ y + 1 = -\frac{2}{5}x - \frac{8}{5} \] 4. **Isolate \(y\)**: \[ y = -\frac{2}{5}x - \frac{8}{5} - 1 \] Convert \(1\) to a fraction with a denominator of \(5\): \[ 1 = \frac{5}{5} \] So, \[ y = -\frac{2}{5}x - \frac{8}{5} - \frac{5}{5} \] \[ y = -\frac{2}{5}x - \frac{13}{5} \] Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = -\frac{2}{5}x - \frac{13}{5}} \]