document.write( "Question 24077: Explain how the constant of variation and the slope are related in a direct variation equation. Please help I'm stuck and need help. \n" ); document.write( "

Algebra.Com's Answer #12818 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Compare the slope-intercept form of a linear equation with an equation for direct variation.\r
\n" ); document.write( "\n" ); document.write( "Slope-intercept form:
\n" ); document.write( " $\"y+=+mx+%2B+b\"$ m is the slope of the line.
\n" ); document.write( "Direct variation:
\n" ); document.write( " $\"y+=+kx\"$ y varies diectly as x. k is the constant of variation.\r
\n" ); document.write( "\n" ); document.write( "Do you see the similarity?\r
\n" ); document.write( "\n" ); document.write( "Let's compare the two equations using numbers:\r
\n" ); document.write( "\n" ); document.write( "Slope-intercept:
\n" ); document.write( " $\"y+=+4x%2B3\"$ The slope (m) is 4 and the y-intercept (b) is 3.\r
\n" ); document.write( "\n" ); document.write( "Direct variation:
\n" ); document.write( " $\"y+=+kx\"$ To find the value of k, you'll need to know the values of y and x. Let's say that y = 8 when x = 2, so that k = y/x = 8/2 = 4. So you can write:
\n" ); document.write( " $\"y+=+4x\"$ \r
\n" ); document.write( "\n" ); document.write( "Now let's graph these two lines and compare them.
\n" ); document.write( " $\"graph%28300%2C200%2C-5%2C5%2C-5%2C5%2C4x%2B3%2C4x%29\"$
\n" ); document.write( "The red line is: $\"y+=+4x%2B3\"$
\n" ); document.write( "The green line is: $\"y+=+4x\"$ \r
\n" ); document.write( "\n" ); document.write( "Conclusion:
\n" ); document.write( "The constant of variation in a direct-variation equation is the slope of the line when the equation is graphed. \n" ); document.write( "

\n" );