document.write( "Question 571128: I have to determine whether the graphs of each pair of lines are parallel...Please help. \n" ); document.write( "

Algebra.Com's Answer #367993 by KMST(5328) $\"\"$ $\"About$

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To find, without graphing, if the graphs of two linear equations are parallel, look at the slopes. If the slopes are the same number, the lines are parallel or the equations could represent the same line. (If the slopes are different, the lines would intersect at just one common point, and if the product of the slopes is -1, the lines are perpendicular).
\n" ); document.write( "To find the slope, you could solve for y to get the slope-intercept form of the equation.
\n" ); document.write( "For example, $\"3x-2y=5\"$ can be solved for y
\n" ); document.write( " $\"3x-2y=5\"$ --> $\"3x-2y%2B2y=5%2B2y\"$ --> $\"3x=5%2B2y\"$ --> $\"3x-5=5%2B2y-5\"$ --> $\"3x-5=2y\"$ --> $\"%281%2F2%29%283x-5%29=%281%2F2%292y\"$ --> $\"%283%2F2%29x-5%2F2=y\"$ or
\n" ); document.write( " $\"y=%283%2F2%29x-5%2F2\"$ , which is the slope-intercept form of the equation.
\n" ); document.write( "The coefficient of x in the slope-intercept form of the equation is the slope. (The independent term, or constant,-5/2 in this case, is the intercept or y-intercept).
\n" ); document.write( "Finding the slope-intercept form of $\"3x-2y=5\"$ tells you that its graph is parallel to the graph of $\"y=%283%2F2%29x%2B4\"$ and that the graph of $\"3x-2y=5\"$ is the same line as the graph of $\"y=%283%2F2%29x-5%2F2\"$ . It also tells you that the graph of $\"3x-2y=5\"$ is not parallel to the graph of any other line that does not have 3/2 as its slope.
\n" ); document.write( "Beware of linear equations like $\"y=%283%2F2%29%28x-1%29-1\"$ because as you simplify it
\n" ); document.write( " $\"y=%283%2F2%29%28x-1%29-1\"$ --> $\"y=%283%2F2%29x-1%283%2F2%29-1\"$ --> $\"y=%283%2F2%29x-3%2F2-2%2F2\"$ --> $\"y=%283%2F2%29x-5%2F2\"$
\n" ); document.write( "you realize that its graph is not a line parallel to the graph of $\"y=%283%2F2%29x-5%2F2\"$ . It is the same line.
\n" ); document.write( "Solving for y and getting the slope from the slope-intercept form of the equation will give you the answer in all cases, except if there is no y in your equation(s). A linear equation with only x and no y, like $\"x=4\"$ , represents a vertical line, which has no slope (its slope is said to be undefined). A vertical line can only be parallel to another vertical line.
\n" ); document.write( "NOTE:
\n" ); document.write( "In some case, you may not need to solve for y.
\n" ); document.write( "For example,
\n" ); document.write( " $\"3x-2y=5\"$ and $\"3x-2y=8\"$ , where the same x-y expression is stated as equal to two different numbers, are parallel. You can see that for the same value of y, x must be 1 more for $\"3x-2y=8\"$ , so its graph is like the other one, but moved 1 unit to the right. \n" ); document.write( "

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