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Difference Between Linear Equations and Linear Inequalities

Consider first a linear equation of the form 2x - 5y = 8.
Now choose a linear inequality of the form 5y < 2x - 8 or 5y > 2x - 8.

What are the major differences between the linear equation graph and the linear inequality graph?

Solution Preview

Consider first a linear equation of the form 2x - 5y = 8

The equation 2x - 5y = 8 is the equation of a line. You can rearrange it so that it's in slope-intercept form:

2x - 5y = 8
-5y = -2x + 8
y = (2/5)x - (8/5)

This line has a y-intercept of -8/5 and a slope of 2/5. The graph is below. It is made up of all the points (x, y) for which the equation holds. For example, the point (1, -6/5) is a point on the line because 2(1) - 5(-6/5) = 8 is true. The point (0, 8) is not on the line because 2(0) - 7(8) = 8 is not true.

Now choose a linear inequality of the form 5 < 2x - 8 or 5 > 2x - 8

Let's look at the first one. You can write this as y < ...

Solution Summary

The solution uses an example of a linear equation and an example of a linear inequality to demonstrate how to graph each kind of relation and the differences between the graphs.

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