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OG11 Diagnostic Que# 39

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OG11 Diagnostic Que# 39

by aimhigh715 » Thu Nov 15, 2007 2:55 pm
In the xy-plane, if line k has negative slope and passes through the point (-5, r), is the x-intercept of line k positive?

1) slope of line k is -5
2) r > 0

OA : E

My question is why? With (1) I understand, slope you will still need either r or y-intercept (y = mx + b) to find the other.

OA explanation of 2) is confusing. knowing that r > 1 means for sure its somewhere in quadrant II... but doesn't 2) guarantee that line K will cross x-intercept at a NEGATIVE point somewhere?

Thanks in advance
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by samirpandeyit62 » Thu Nov 15, 2007 10:10 pm
the xy-plane, if line k has negative slope and passes through the point (-5, r), is the x-intercept of line k positive?


the pt (-5,r) will lie in the 2nd or 3rd quadrant

so x intercept maty be +ve, -ve or 0

1) slope of line k is -5

does not have much significance, as depending upon r so it can have +ve & -ve or 0 x inetercept INSUFF

2) r > 0

pt is in 2nd quadrant

still it can have +ve, -ve inetecept & 0 intercept

combine : pt is in 2nd Q & slope =-5 here also all three possibilties will exist depending upon value of r

If it is difficult to visualise this a good appraoch would be to evaluate the pts with the slope using the std line eqn form

i.e y =mX + c

plug in values of slope & the pts for & try with some + ve vals of r u will be able to deduce that all three posiibilties can arise
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Samir
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by aimhigh715 » Fri Nov 16, 2007 11:41 pm
Thanks given, TY Samir!

Dunno how I missed it earlier, must've been one of those questions towards the end of a 3 hour session when I'm dizzy =) I can definitely visualize the line w/ a -ve slope having a +ve x-intercept now. Cheers.
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