# Slopes, Rates of Change, and Similar Triangles

In this lesson, you will learn a formula to compute the slope of a line using any two points on the line (not just points whose $x$-coordinates differ by 1). You will also use similar triangles to see why this formula works, and why the line with slope $m$ and $y$-intercept $(0, b)$ is the graph of the equation $y=mx+b$.

## Slope as rate of change

Jane is descending a 20-foot rock. She climbs down the rock at a rate of 2 feet per minute (so, each minute her height decreases by 2 feet).

In this example $t$ represents time in minutes and $h$ represents Jane’s height in feet. When $t=0$, $h=20$. What is $h$ when $t=1$? Enter the value you just found in the $h$ column corresponding to $t=1$ in the table to the right. Repeat this for the other $t$ values in the table to chart her progress. The points representing Jane’s height are plotted on the grid to the left.