Previously you learned that if you plot at least two ordered pairs on the coordinate plane, you can use a straightedge to connect those two points and create a line. The steepness of that line is called its slope.
The slope of a line is a measurement of how the rise of the line changes as you read the run of the line from left to right. The larger the magnitude of the slope value, the steeper the line. You can calculate the slope of a line using the slope formula.
The slope formula is \( m = \frac{\text{rise}}{\text{run}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \).
In this formula, \( (x_{1},\ y_{1}) \) represent the coordinates of one known point on the line, and \( (x_{2},\ y_{2}) \) represent the coordinates of the other known point on the line.
Slope is also sometimes explained as the vertical change in the line compared to the horizontal change in the line. Keep in mind that a slope value can be positive or negative. For example:
What is the slope of the line that connects the ordered pairs \( ( - 4, - 18) \) and \( (2,\ 12) \)?
The slope is 5.
Step 1: Label the given ordered pairs as \( (x_{1},\ y_{1}) \) and \( (x_{2},\ y_{2}) \). |
Let \( \left( x_{1},\ y_{1} \right) = ( - 4, - 18) \) Let \( \left( x_{2},\ y_{2} \right) = (2,\ 12) \) Remember that it does not matter which ordered pair is assigned to be \( (x_{1},\ y_{1}) \) or \( (x_{2},\ y_{2}) \). |
Step 2: Substitute the values into the slope formula. |
\( m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \) \( m = \frac{\left( 12 \right) - ( - 18)}{\left( 2 \right) - ( - 4)} \) \( m = \frac{12 + 18}{2 + 4} \) \( m = \frac{30}{6} \) \( m = 5 \) |
How well can you use the formula to calculate the slope of a line? Use the activity below to practice. Find the slope of the line that connects the ordered pairs on each slide, then check your answer.
