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Determining the Slope of a Line

Introduction

What is Slope?

Slope is a measure of rate of change. The slope of a line describes how much the line increases or decreases on the y-axis over a certain amount of change on the x-axis.

Slope Formula

You can find the slope of a line between two points by finding the difference in the y-values over the difference in the x-values. This results in the following formula:

Determining Slope from a Graph

When given a graph of a linear equation, you can determine the slope of the line by looking at the change in y and the change in x between two points on the graph.

Using Coordinate Points

We can also determine the slope of the line by using the equation for slope with any two coordinate points that are on the line. Looking at the previous graph, we can see that the line passes through the coordinate points (3, 5) and (6, 7). Using these points, we can put the x- and y-values into the slope formula to calculate the slope.

Let’s look at another example:

Line A passes through the points (1, 4) and (−1, 7). Find the slope of Line A.

To find the slope, we can plug in the x- and y-values for each coordinate point into the formula for slope:

$\textup{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\textup{Slope}=\frac{(7)-(4)}{(-1)-(1)}=\frac{3}{-2}=-\frac{3}{2}$

Notice that it does not matter which y-value we choose for y₂ and y₁. As long as we use the corresponding x-values for x₂ and x₁, the slope will be the same:

$\textup{Slope}=\frac{(4)-(7)}{(1)-(-1)}=\frac{-3}{2}=-\frac{3}{2}$