document.write( "Question 77929: . Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 2y = 8 and passing through (1, -6).
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\n" ); document.write( "Cant figure this one out either, Help. \n" ); document.write( "

Algebra.Com's Answer #55838 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, it is often helpful to rewrite the given equation (x+2y = 8) in slope-intercept form: y = mx+b
\n" ); document.write( " $\"y+=+%28-1%2F2%29x+%2B4\"$ Do yo see how to get this?
\n" ); document.write( "Comparing this with the slope-intercept form:
\n" ); document.write( " $\"y+=+mx%2Bb\"$ you can see that the slope of the given line is $\"%28-1%2F2%29\"$
\n" ); document.write( "Now, you will no doubt recall that perpendicular lines have slopes that are the negative reciprocal of each other.
\n" ); document.write( "So, the slope of the new line, because it is perpendicular to the given line, will be: $\"2\"$ which is the negative reciprocal of $\"%28-1%2F2%29\"$
\n" ); document.write( "Now you can write, for the new line, the equation:
\n" ); document.write( " $\"y+=+2x%2Bb\"$ But we're not quite done because we need to find the value of b, the y-intercept. We are given the ordered pair of a point (1, -6) through which the new line passes. We can use the x- and y-coordintaes of this point to find the value of b for the new line.
\n" ); document.write( "Substitute the x- and y-values from the point into the equation (y= 2x+b) and solve for b.
\n" ); document.write( " $\"-6+=+2%281%29+%2B+b\"$ Subtract 2 from both sides.
\n" ); document.write( " $\"-8+=+b\"$ Now we can finish the equation of the new line:
\n" ); document.write( " $\"y+=+2x-8\"$
\n" ); document.write( "One final step to do because you need your answer in standard form: $\"ax%2Bby+=+c\"$
\n" ); document.write( " $\"2x-y+=+8\"$
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