Examples graphs of equations and inequalities
Below are some example graphs of common equations and inequalities that you are likely to encounter.
When looking at these charts, notice how inequalities with the less than or equal to sign or the greater than or equal to sign consist of a solid line. That means that the points in that equation lie not only in the shaded region of the graph but also the line itself. While inqualities such as greater than or less than will consist of a dotted line. This means that the vectors in the inequality will never be on the line but rather above or below the line, that is, in the shaded region.
One way to utilize these charts is to set up your equation in slope intercept form when both the dependent variable, independent variable and constant are present. If you don't have all three values, then look for the chart that best represents your equation. Write out your equation by trying to keep y on one side of the equation or inequality and x and/or k on the other. If y is not present, then try getting your equation or inequality where x is on one side and k on the other. Search for the sample graph below. If you are tackling a word problem or real life problem, ask yourself if it makes sense for your data points (vectors) to lie in the shaded regions (or solid line when present).
Without wasting more time, the chart examples are presented below.
y = mx + b
y >= mx + b
y <= mx + b
y > mx + b
y < mx + b
y = k
y >= b
y <= b
y > b
y < b
x = k
x >= k
x <= k
x > k
x < k
That is pretty much it. If you need a graph to a particular equation or inequality, leave a comment with your equation and I will do my best to reply asap with a solution.
