You can put this solution on YOUR website! This one checks your understanding of graphing.
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The graph of x = -9 is a vertical line through the point -9 on the x-axis.
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You can interpret this line as meaning that the value of x is always -9 for any point
on the graph.
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The slope of a vertical line is undefined. Note that undefined is not the same as zero.
A line with zero slope is a horizontal line.
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Recall that the equation for slope is:
.
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But for the equation you were given and because x is always
the same value. Therefore, the equation for the slope becomes:
.
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and if you simplify the denominator by combining terms, it becomes 0. But in algebra
division by zero is not permitted. Therefore, the slope of the vertical line is classified
as undefined.
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Notice also that since the graph of x = -9 is a vertical line, it is parallel to the y-axis.
And from geometry ... parallel lines never intersect. Therefore, the graph never
intersects the y-axis.
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Hope this helps you to understand the characteristics of the graphs when you have an
equation that defines x as being equal to some constant. The graph will be vertical,
will have an undefined slope, and will not intersect the y-axis.
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