What is an equation of the line that passes through the points \( (5,-6) \) and \( (-5,-2) \) ?

To find the equation of the line that passes through the points \( (5,-6) \) and \( (-5,-2) \), we first calculate the slope \( m \) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in our points, we find \( m = \frac{-2 - (-6)}{-5 - 5} = \frac{4}{-10} = -\frac{2}{5} \). Next, we can use the point-slope form of a line, \( y - y_1 = m(x - x_1) \). Using point \( (5, -6) \), we get \( y + 6 = -\frac{2}{5}(x - 5) \). Simplifying, we have \( y = -\frac{2}{5}x - 4 \). Thus, the equation of the line is \( y = -\frac{2}{5}x - 4 \). One fun fact about linear equations is that they can also represent many real-world situations—think about things like speed over time or budgeting. They help us visualize relationships and trends, making it easier to grasp changes and predict outcomes! Also, when solving for equations and slopes, always double-check your calculations; errors in arithmetic can lead you astray. A common mistake is misplacing the negative sign or confusing which point to use first—taking a moment to verify your work can save you from headaches down the line!