What is an equation of the line that passes through the points \( (-1,7) \) and \( (1,-3) \) ?

To find the equation of the line that passes through the points \((-1, 7)\) and \( (1, -3)\), we first calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in the points, we have: \[ m = \frac{-3 - 7}{1 - (-1)} = \frac{-10}{2} = -5 \] Now, we can use the point-slope form of the line’s equation \(y - y_1 = m(x - x_1)\). Using point \((-1, 7)\): \[ y - 7 = -5(x + 1) \] Expanding this gives: \[ y - 7 = -5x - 5 \\ y = -5x + 2 \] So, the equation of the line is \(y = -5x + 2\). For a little fun, did you know the concept of a slope is often visually represented on a graph? If you think of a mountain, a steep slope means a steep climb! A linear equation like this tells you how y changes as x does—just like navigating a hilly terrain! Now, if you're looking to understand more about why lines are straight or how they make shapes in algebra, reading about transformations in geometry could be a keen next step! Exploring how different equations represent various shapes can really elevate your mathematical journey.