How do you calculate slope from a graph?
Nuzhat has already discussed how you can find the slope of a line from two points that lie on the line. I'll discuss two other methods of finding the slope from a graph.
1. From the angle made with the x-axis
Since the slope of a line is basically the ratio of the y-component of the line to its x-component,
The slope of a line can be found out by taking tangent of the angle between the given line and the x-axis.
Consider the following figure:
In this case, the angle between the x-axis and the line is
Therefore, Note: Angles in the counterclockwise direction are taken as positive, and those in the clockwise direction are taken as negative.
For example, if the angle between the x-axis and the given line is Slope of the given line = 2. From the equation of the line The slope of a line can also be determined from its equation. The standard form of the equation of a line is: where First, the equation of the line must be written in the standard form. Then, the slope of the line = For example, let the equation of the given line be Rewriting in the standard form, we get: Therefore, the slope of the line
Slope of the given line =
and we can see that:
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To calculate the slope from a graph, you need to choose two points on the graph and then use the formula:
[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} ]
You can find the change in ( y ) by subtracting the ( y )-coordinates of the two points, and find the change in ( x ) by subtracting the ( x )-coordinates of the two points. Then, divide the change in ( y ) by the change in ( x ) to get the slope.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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