With slope \( -\frac{7}{8} \), through \( \left(0, \frac{9}{7}\right) \)

To write the equation of a line with a slope of \(-\frac{7}{8}\) that passes through the point \((0, \frac{9}{7})\), you can use the point-slope form of a linear equation. Since the \(y\)-intercept is the \(y\) value at \(x = 0\), the equation directly can be expressed as \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. Plugging in the values, you get \(y = -\frac{7}{8}x + \frac{9}{7}\). Think of slope as your go-to guide for how steep your line is! It tells you how many units you move up or down for each unit you move to the right. In real life, this could represent anything from bank interest rates to road inclines. So next time you're on a hill, consider that slope! If you're plotting, be wary of sign errors when calculating slope or y-intercepts! A negative slope means your line will go down from left to right. Remember to always double-check your points; a simple mix-up can turn a perfectly good answer into a head-scratcher!