From the graph of x = 4 find the characteristics of the line.

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mathappeal | High School Teacher | (Level 1) Adjunct Educator

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The equation tells us that x always equals 4.  This is a constraint on the value of x.  However, there are no restrictions on what the value of y can be, so once one is at 4 on the x-axis (4,0), there is an infinite number of points both positive and negative which create a line parallel to, and four units to the right of, the y-axis, a vertical line.

The slope of a vertical line is UNDEFINED.  Why is that so?  If you have a line with a positive slope, and you make it steeper and steeper so that the [absolute] value of y is increasingly greater than the [absolute] value of x, you eventually will approach a limit of positive infinity.  If you do the same thing with a negatively-sloped line, you eventually will approach a limit of negative infinity.  A number cannot be infinitely positive and infinitely negative at the same time, so that is why the slope of a vertical line is undefined.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The graph of the line given is x = 4. This is a straight line with the x-coordinate of all the points on the line equal to 4. The line is therefore parallel to the y-axis.

The x-intercept of the line is (4, 0). As it is parallel to the y-axis, it does not intersect the y-axis.

The slope of the line is infinity.