In the previous section, we used a graph to determine the relationship between the number of times a cricket chirps (in one minute) and the temperature (in degrees Fahrenheit).
\[slope=\frac{\Delta y}{\Delta x} =\frac {rise}{run}=\frac {1}{4}\]
In this module, we have used tables and graphs to determine slopes. In Lesson 1, we made connections between the changes in \(y\) and \(x\) to develop the slope formula.
When two points can be determined in a linear relationship, using the slope formula is a quick and efficient way to calculate slope.
- The formula for finding the slope between any two points on a line, where the first point is defined as \((x_1,y_1)\) and the second point is defined as \((x_2,y_2)\), is shown as: \[slope=\frac{(y_2-y_1)}{(x_2-x_1)}\]
Example: Use the slope formula to find the slope of the line that passes through the points \((-3, -2)\) and \((3, -5)\).
- Point 1: \((-3, -2)\) where \(x_1=-3\) and \(y_1=-2\)
- Point 2: \((3, -5)\) where \(x_2=3\) and \(y_2=-5\)
\[slope=\frac{-5-(-2)}{3-(-3)}=\frac{-5+2}{3+3}=\frac{-3}{6}=-\frac{1}{2}\]
1. Use the Slope Formula to calculate the slope between the two points from our previous graph:
Point \(1\ (80,57)\) and Point \(2 \ (184,83)\)
For more instruction, go to Watch (Calculating Slope). After you finish watching the video close the page to return to this page.
