
x and yIntercepts The graphical concept of x and yintercepts is pretty simple. The xintercepts are where the graph crosses the xaxis, and the yintercepts are where the graph crosses the yaxis. The problems start when we try to deal with intercepts algebraically. To clarify the algebraic part, think again about the axes. When you were first introduced to the Cartesian plane, you were shown the regular number line from elementary school (the xaxis), and then shown how you could draw a perpendicular number line (the yaxis) through the zero point on the first number line. Take a closer look, and you'll see that the yaxis is also the line "x = 0". In the same way, the xaxis is also the line "y = 0". Then, algebraically,
More specifically,
Using the definitions of the intercepts, I will proceed as follows: xintercept(s): y = 0 for the xintercept(s), so: 25x^{2} + 4y^{2} = 9 Then the xintercepts are the points (^{ 3}/_{5}, 0) and (^{ –3}/_{5}, 0) yintercept(s): Copyright © Elizabeth Stapel 19992011 All Rights Reserved x = 0 for the yintercept(s), so: 25x^{2} + 4y^{2} = 9 Then the yintercepts are the points (0, ^{3}/_{2} ) and (0, ^{–3}/_{2} ) Just remember: Whichever intercept you're looking for, the other variable gets set to zero. In addition to the above considerations, you should think of the following terms interchangeably: "xintercepts" = "roots" = "solutions" = "zeroes" In other words, the following exercises are equivalent:
If you keep this equivalence in the back of your head, many exercises will make a lot more sense. For instance, if they give you something like the following graph: ...and ask you to find the "solutions", you'll know that they mean "find the xintercepts", and you'll be able to answer the question, even though they were clumsy in their use of the mathematical terms, and they never gave you the equation.


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