document.write( "Question 471982: in the xy plane , line k is a line that does not pass through the origin.
\n" ); document.write( "which of the following statements individually provides sufficient additional information to determine whether the slope of line k is negative?\r
\n" ); document.write( "\n" ); document.write( "indicate all such statements.
\n" ); document.write( "(a) the x intercept of line k is twice the y intercept of line k?
\n" ); document.write( "(b) the product of the x intercept and the y intercept of the line k is positive?
\n" ); document.write( "(c) line k passes through the points (a,b) and (r,s) where (a-r)(b-s)<0 \n" ); document.write( "

Algebra.Com's Answer #323778 by richard1234(7193) $\"\"$ $\"About$

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a) If the line goes through the points (2z,0) and (0,z) then the slope is z/(-2z) = -2. This works for all nonzero z, so a) works.\r
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\n" ); document.write( "\n" ); document.write( "b) Let (x,0) and (0,y) denote the x- and y-intercepts. The slope is obviously -y/x. Given that xy is positive, then x,y are either both positive or both negative, and the quotient y/x is also positive. However the slope of k is -y/x so this is negative, so b) works.\r
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\n" ); document.write( "\n" ); document.write( "c) The slope of the line k is (b-s)/(a-r) (the order of which we choose the points does not matter). Since (a-r)(b-s) < 0, it follows that exactly one of a-r or b-s is negative, and the slope of k is also negative (similar scenario as part b)).\r
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\n" ); document.write( "\n" ); document.write( "Hence, all three statements work. \n" ); document.write( "

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