document.write( "Question 271277: i have a problem that says solve for k where the equation is 4x-ky-7=0 and the slope is = to 3. How do I solve for k? \n" ); document.write( "

Algebra.Com's Answer #198622 by jsmallt9(3758) $\"\"$ $\"About$

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There are a couple of ways to solve this problem:

First, this equation is (or is nearly) in standard form. And there is a formula for the slope of an equation in standard form: $\"m+=+-A%2FB\"$ . Since the slope, m, is 3 and A = 4 and B = -k, this formula for this equation is
\n" ); document.write( " $\"3+=+-4%2F%28-k%29+=+4%2Fk\"$
\n" ); document.write( "We can solve this for k. Multiply both sides by k:
\n" ); document.write( " $\"3k+=+4\"$
\n" ); document.write( "Divide both sides by 3:
\n" ); document.write( " $\"k+=+4%2F3\"$
Solve for y first. (You'll see why when we get there.
\n" ); document.write( " $\"4x-ky-7+=+0\"$
\n" ); document.write( "I'll start by adding ky to each side:
\n" ); document.write( " $\"4x+-+7+=+ky\"$
\n" ); document.write( "Instead of dividing by k I am going to multiply both sides by 1/k. Multiplying by the reciprocal of k is equivalent to dividing by k. But it leaves the equation in a much better form:
\n" ); document.write( " $\"%281%2Fk%29%284x+-+7%29+=+%281%2Fk%29%28ky%29\"$
\n" ); document.write( "Using the Distributive property on the left side we get:
\n" ); document.write( " $\"%284%2Fk%29x+-+7%2Fk+=+y\"$
\n" ); document.write( "We have solved the equation for y. This puts the equation in Slope-intercept form. The slope is coefficient of x: 4/k. The slope is supposed to be 3 so:
\n" ); document.write( " $\"3+=+4%2Fk\"$
\n" ); document.write( "Solving this for k we get:
\n" ); document.write( " $\"k+=+4%2F3\"$

\n" ); document.write( "The first way was easier but it requires that you know the slope formula for equations of lines in Standard Form. \n" ); document.write( "

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