Question 120991: What would be the slope and y-intercept in the following equation: x = -8? I got: Slope: 0; y-intercept: none. Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! You were on the right track, but a little bit in error on how you interpreted the slope.
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Go back to the definition of slope ... slope is the change in y divided by the corresponding
change in x. When you say that x = -8 that tells you that the change in x is zero ... x is
always -8 regardless of what the value of y is. But if the change in x is zero, then the
definition of slope becomes "the change in y divided by zero." And algebra tells us that
division by zero is not allowed. Therefore, the slope is undefined for this problem.
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If the slope was zero, then the graph would be a horizontal line, and there would then have
to be a y-intercept. But you were correct when you said that the y-intercept is none. Why is
that the case? It is because the graph of x = -8 is a vertical line ... a line of undefined
slope.
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The following graph shows in "brown-red" color the graph of x = -8. You can see that it
is perpendicular to the x-axis and, therefore, cannot intercept the y-axis. I've added as a
green graph an example of a line that has zero slope just to show you the difference
between an undefined slope and a zero slope.
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Hope this helps you to see the correct interpretation of an equation that says x equals some
constant value.
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