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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. $m=x_{2}−x_{1}y_{2}−y_{1} $ In the above equation, $(x_{1},y_{1})$ and $(x_{2},y_{2})$ represent two points on the line. Let's substitute them by $(2,3)$ and $(5,2).$$m=x_{2}−x_{1}y_{2}−y_{1} $

$m=5−22−3 $

SubTermsSubtract terms

$m=3-1 $

MoveNegNumToFracPut minus sign in front of fraction

$m=-31 $

b

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

Since the graph is parallel to the $x$-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, $0.$ $m=0$ Here we will show how it can be proved that the slope really is $0.$ We will then use the slope formula. $m=x_{2}−x_{1}y_{2}−y_{1} $ Let's find two points on the graph, $(x_{1},y_{1})$ and $(x_{2},y_{2}),$ that we can use in the slope formula.

We will use the points $(2,2)$ and $(5,2)$ to find the slope. As we expected, the slope formula returned that the slope is $0.$ c

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. $m=x_{2}−x_{1}y_{2}−y_{1} $ 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 $m=21 $ means that for every $2$ steps in the positive horizontal direction, the graph travels $1$ step in the positive vertical direction.