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Calculating the first difference of a linear relation.
Let's look at an example.
Below is a table of values for the
following linear relation, Y equals X plus 3.
Calculate the first differences for the data by subtracting the values of Y.
So, 2 minus
1 equals 1.
And then, look at the next difference,
3 minus 2 equals 1, and then subtract
4 minus 3, which equals 1.
And lastly, subtract 5 minus 4, which equals 1.
Since the first differences are the same,
the graph for this equation will be linear.
Let's plot the points of the graph.
This is the x-axis and this is the y-axis.
So, negative two on the X axis and up one on the Y axis is your first point.
And negative one and two, and zero and three, and one and four.
And 2 and up to 5 on the y-axis.
Next, draw a straight line connecting your points.
[BLANK_AUDIO]
Three reasons why the graph is linear for the equation y equals x plus three.
The first reason is, I graph the points and the graph is a straight line.
So, graph
equals straight
line.
The second reason is, the exponent on the x is 1.
So exponent on
the x equals 1.
And the third reason is the first differences are constant.
First differences
are constant.