Question 184558
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The process for finding the intercepts requires substituting 0 for each of the variables and then determining the value of the other variable to give you two points: (a,0) which is the <i>x</i>-intercept (the point where the graph intersects the <i>x</i>-axis and (0,b) which is the <i>y</i>-intercept.  This would give you two points that will define the line that is the graph of your equation.


For this equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = 0 \ \ \Rightarrow\ \ y = -5(0) = 0]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y = 0 \ \ \Rightarrow\ \ x = \frac{0}{-5} = 0]


The problem you have with the given equation is that the <i>x</i>- and <i>y</i>-intercepts are the same point, namely the origin (0,0), and one point is insufficient to define a line.  Consequently, just finding the intercepts is not enough to create the graph of this equation.


To find a second point on the line, you need to find a point that is <i><b>not</b></i> an intercept.  Select a value for <i>x</i> other than 0, substitute that value, and determine the resulting value for <i>y</i>.  The selected value and the resulting value can be formed into an ordered pair that you can graph to establish your second point. (I chose 1 as a value for <i>x</i>, but you could choose anything you like so long as it is not 0)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = 1 \ \ \Rightarrow\ \ y = -5(1) = -5]


Now you have two points, (0,0) and (1,-5).  Plot them then draw a line through them to give you your graph.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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