How to find the slope of ordered pairs?
Understand the Problem
The question is asking for the method to calculate the slope given a set of ordered pairs. The slope is typically calculated using the formula (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).
Answer
The slope $m$ is equal to $2$.
Answer for screen readers
The slope $m$ is equal to $2$.
Steps to Solve
- Identify the Ordered Pairs
First, you need to identify the two ordered pairs you will use to calculate the slope. Let's say the ordered pairs are $(x_1, y_1)$ and $(x_2, y_2)$.
- Use the Slope Formula
Use the formula for calculating the slope given by $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Here, $m$ represents the slope.
- Substitute the Values
Substitute the values of the ordered pairs into the slope formula. For example, if the ordered pairs are $(2, 3)$ and $(4, 7)$: $$ m = \frac{7 - 3}{4 - 2} $$
- Calculate the Results
Perform the arithmetic in the numerator and the denominator: $$ m = \frac{4}{2} $$
- Simplify the Fraction
Finally, simplify the fraction to find the slope: $$ m = 2 $$
The slope $m$ is equal to $2$.
More Information
The slope represents the rate of change between the two points and is a measure of how steep the line is. A positive slope indicates that as $x$ increases, $y$ also increases.
Tips
- Mixing up the points when substituting values, which can lead to an incorrect calculation of the slope.
- Forgetting to simplify the fraction resulting from the slope calculation.
