A linear equation is an equation with two variables whose graph
is a line. The graph of the linear equation is a set of points in
the coordinate plane that all are solutions to the equation. If all
variables represent real numbers one can graph the equation by
plotting enough points to recognize a pattern and then connect the
points to include all points.
If you want to graph a linear equation you have to have at least
two points, but it's usually a good idea to use more than two
points. When choosing your points try to include both positive and
negative values as well as zero.
Example:
Graft the function y = x + 2
Begin by choosing a couple of values for x e.g. -2, -1, 0, 1 and
2 and calculate the corresponding y values.
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x
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y = x + 2
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Ordered pair
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-2
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-2 + 2 = 0
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(-2, 0)
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-1
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-1 + 2 = 1
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(-1, 1)
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0
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0 + 2 = 2
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(0, 2)
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1
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1 + 2 = 3
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(1, 3)
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2
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2 + 2 = 4
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(2, 4)
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Now you can just plot the five ordered pairs in the coordinate
plane
At the moment this is an example of a discrete function. A
discrete function consists of isolated points.
By drawing a line through all points and while extending the
line in both directions we get the opposite of a discrete function,
a continuous function, which has an unbroken graph.
If you only want to use two points to determine your line you
can use the two points where the graph crosses the axes. The point
in which the graph crosses the x-axis is called the x-intercept and
the point in which the graph crosses the y-axis is called the
y-intercept. The x-intercept is found by finding the value of x
when y = 0, (x, 0), and the y-intercept is found by finding the
value of y when x = 0, (0, y).
Video lesson: Find the values of x and draw
this equation in a graph