What is an equation of the line that passes through the points \( (-8,1) \) and \( (-7,0) \) ? Answer Attempt 1 out of 3

To find the equation of the line that passes through the points \( (-8,1) \) and \( (-7,0) \), we start by calculating the slope \( m \) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{-7 - (-8)} = \frac{-1}{1} = -1. \] Now, using the point-slope form \( y - y_1 = m(x - x_1) \) with one of the points, we choose \( (-8, 1) \): \[ y - 1 = -1(x + 8). \] Simplifying this, we find: \[ y - 1 = -x - 8 \implies y = -x - 7. \] So, the equation of the line is \( y = -x - 7. \) If you're ever trying to find the equation of a line from two points, remember that your first step should be the slope calculation. It's a bit like putting together a puzzle where the slope is your missing piece, helping you connect the dots accurately! When graphing this line, it’s useful to plot both points to visualize how the line cuts through the coordinate plane. Drawing arrows on either end can emphasize that the line extends indefinitely in both directions, making it easier to see the relationship between the x and y coordinates!