document.write( "Question 124770: Write the equation in either slope-intercept form or standard form:\r
\n" ); document.write( "\n" ); document.write( "The vertical line through the point(-45,61) \n" ); document.write( "

Algebra.Com's Answer #91465 by solver91311(24713) $\"\"$ $\"About$

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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 $\"x=a\"$ . Notice that y is not part of the equation. That is because as long as $\"x=a\"$ , 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 $\"x=-45\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Also, note that this equation is written in standard form ( $\"ax%2Bby=c\"$ ). 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 ( $\"%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29\"$ ), hence the slope is undefined. If you cannot define m, you cannot write $\"y=mx%2Bb\"$ . You also do not have an intercept because the vertical line is parallel to the y-axis and therefore never intersects it.\r
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\n" ); document.write( "\n" ); document.write( "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 $\"y=b\"$ . x does not form part of the equation because it doesn't matter what x equals, y is always equal to b. \n" ); document.write( "

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