Find an equation for the line that passes through the points \( (-1,6) \) and \( (5,2) \).

To find the equation of the line passing through the points \((-1, 6)\) and \((5, 2)\), we first need to calculate the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{2 - 6}{5 - (-1)} = \frac{-4}{6} = -\frac{2}{3} \] Now, we can use the point-slope form \(y - y_1 = m(x - x_1)\) with one of the points, say \((-1, 6)\): \[ y - 6 = -\frac{2}{3}(x + 1) \] Distributing and simplifying gives: \[ y - 6 = -\frac{2}{3}x - \frac{2}{3} \] Adding 6 to both sides: \[ y = -\frac{2}{3}x + \frac{16}{3} \] So, the equation of the line is \(y = -\frac{2}{3}x + \frac{16}{3}\). Fun Fact: This method of using the point-slope formula can be such a lifesaver when you're racing against the clock in math tests! Not only does it streamline the process, but it also helps you visualize the line quickly. For those keen on precision, a common mistake is forgetting to simplify when adding or subtracting fractions. Double-check all arithmetic, and you’ll avoid unnecessary errors that can sour the sweetness of getting the right equation!