The Slope Of A Straight Line
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SAMPLE LESSON
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Recall that a straight line has the formula <Sign in to see all the formulas> or more commonly <Sign in to see all the formulas> where $m$ is the slope of the straight line and $b$ is the y-intercept. The slope between any two points $x_1$ and $x_2$ can be found by taking the "rise" over the "run":
<Sign in to see all the formulas>
In the algebra above, not only did we tell you how to calculate the slope of a straight line, but we also showed something unique about a straight line. Since $x_2$ and $x_1$ were both arbitrary, we have shown that the slope of the straight line never changes along the x-axis. This should be visually obvious. In the picture below, we have calculated the slope at two different points for the straight line <Sign in to see all the formulas>. Note that no matter where we calculate the "rise" and the "run", the slope is always the same.
Now let's do the same slope calculation with $x^2$:
<Sign in to see all the formulas>
For example, if we calculate the slope between <Sign in to see all the formulas> and <Sign in to see all the formulas> then the slope would be <Sign in to see all the formulas>. Also, if we calculate the slope between <Sign in to see all the formulas> and <Sign in to see all the formulas> then the slope would be <Sign in to see all the formulas>. This emphasizes the point that for <Sign in to see all the formulas> the slope of the function changes depending on where we calculate it. This is true for all functions that are not a straight line.
