What is the slope and y-intercept of the line #x = -5#?

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Answer 1 · 2016-08-26T19:54:36

This equation is a vertical line.

Which means that, regardless of the value of y, x is always #- 5#.

It has no y-intercept because it never crosses the y-axis.
It just goes up and down (theoretically forever) at the x-value of #- 5#.

This equation also has an undefined slope. Slope is the Rise over the Run, right?

#(y2 - y1)/(x2 - x1)#

Suppose y2 = 5 and y1 = 3. Then the Rise is 2 for every change in x-value.

But x doesn't change. For the Run, you can't choose two DIFFERENT values for x. X is always - 5.

If you subtract # -5 - (-5),# you get zero, and division by zero is undefined.

A vertical line has an undefined slope.

So the equation #x = -5# has no defined slope and no y-intercept.