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Determining the Slope of a Line

Determining the Slope of a Line 1.3 - Solution

arrow_back Return to Determining the Slope of a Line

Observing the given graph, we can see that the line is decreasing over its entire interval.

Thus, the graph has a negative slope. Next we need to find two points on the graph.

When two points on a line are known the slope can be calculated by using the slope formula. In the above equation, and represent two points on the line. Let's substitute them by and
We have found that the line has the slope

When we look at the graph, we can see that the line is everywhere at the same distance from the -axis.

Since the graph is parallel to the -axis we say that it is a horizontal line. Next we wish to find the slope of the graph. Once it has been established that a line is horizontal it is not necessary to calculate its slope. That is because all horizontal lines have the same slope, Here we will show how it can be proved that the slope really is We will then use the slope formula. Let's find two points on the graph, and that we can use in the slope formula.

We will use the points and to find the slope.
As we expected, the slope formula returned that the slope is

In this graph we can see that the line is increasing over its entire interval.

A line which is increasing has a positive slope. Next, we want to find the slope of the line. For this we will use the slope formula. We need to find two points on the graph as these are needed in the slope formula.

Let's substitute the points into the equation and solve for the slope.
A slope of means that for every steps in the positive horizontal direction, the graph travels step in the positive vertical direction.