Question 124770: Write the equation in either slope-intercept form or standard form:
The vertical line through the point(-45,61)
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! A vertical line has the characteristic that the x-coordinates of every point on the line are equal. So the vertical line through (a, b) has an equation  . Notice that y is not part of the equation. That is because as long as , the value of y can be any real number. To put it another way, if you are given an equation that graphs to something other than a vertical line, and you choose a specific value for x, there will be exactly one corresponding value for y. Not so with a vertical line -- for the single possible value for x there are infinite choices for y. In your case, the equation would be  .
Also, note that this equation is written in standard form ( ). In your case, a = 1, b = 0, and c = -45. This equation cannot be written in slope-intercept form. Since all of the x-coordinates are equal, the denominator of the slope calculation would be zero ( ), hence the slope is undefined. If you cannot define m, you cannot write  . You also do not have an intercept because the vertical line is parallel to the y-axis and therefore never intersects it.
Contrast this with a horizontal line. In a horizontal line, all of the y-coordinates are equal, regardless of the value of x. So a horizontal line through (a, b) would be  . x does not form part of the equation because it doesn't matter what x equals, y is always equal to b.
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