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Question 252205: For what values of x will the graph of 2x - 3y + 5 = 0 be above the x-axis?
Answer by Jaggkneio(1)   (Show Source):
You can put this solution on YOUR website! First you must rearrange your equation. Equations must be balance. Understanding how to balance them can be difficult, because you must apply abstract rules to balance them. Please remember that these type of equations refer to the cartusian graph (which looks like a cross between a hunters scope and a large plus sign).
This equation can be placed into 2 "equation" forms to help you solve this. The standard form and the Y-intercept form. Again the forms themselves are abstract and must be memorized. The standard form (again to be memorized) is x+y=0 . the " = " makes the an equation. In order to get your problem to standard form, we apply a function to both the left and right of the equation. You could think of it as two children, one on each side of the " = " sign. Each child will not be satisfied unless they have the exact same toy or treat.
2x - 3y + 5 = 0. We must find a way to move the +5 from the left side of the equation to the right side. We must subtract 5 from both sides. 2x - 3y + 5-5 = 0-5. We now have 2x-3y=-5 ( the standard form).
We must go another step forward for this to be plotted on the (cartusian) graph and complete you answer. We must convert this into the Y-intercept form. Y=mx+b, we add an m and b. The M stands for slope and B stands for the y- intercept.
This involves the same rule of applying the exact same function to both sides of the equation. When we are finished the Y will be all by itself on the left side of the " = " sign. 2x-3y=-5. First let's subtract 2x from both sides to get. 2x-2x-3y=-5-2x. The result : -3y=-5-2x . We next need to put into the y-intercept form. -3y=-2x-5. Our next move is to get the Y by itself. To do this we must divide -3 into -3y to wind up with y alone. -3y/-3=(-2x/-3)[-5/-3]. Remember 2 negatives become a positives. Our answer : y=2/3x+5/3 .
You now can plot this on your graphing calculator and take all values above the x-axis (or all positive y a-axis numbers). Manually you can do this by substituting any positive number for y and completing the calculation.
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