# Line slope word problem

by mindauggas
Tags: line, slope, word
P: 634
 Quote by mindauggas His equation was: y=mx+3-4m This becomes: $y=\frac{3}{4-x}(x)+3-4\frac{3}{4-x}$ (???) Then $y=\frac{3}{4-x}(x)-1$ This is the slope-intercept form, so b=-1, but this is clearly absurd ... any suggestions?
^You made a mistake in going from the first equation to the second equation there.

Remember what the question is: Find the possible slopes. The equation of line in #12 is in terms of the slope (represented by m). Your next step should be to obtain x and y intercepts in terms of this slope m.
P: 127
 Quote by Sourabh N ^You made a mistake in going from the first equation to the second equation there. Remember what the question is: Find the possible slopes. The equation of line in #12 is in terms of the slope (represented by m). Your next step should be to obtain x and y intercepts in terms of this slope m.
$x_{intercept}$ 0=mx+3-4m >> $-3=m(x-4)$ >> $\frac{-3}{x-4}=m$ (i don't see any way where the variable x would be on the left by itself ... is there one?)

$y_{intercept}$ y=3-4m

Is this correct? Whats the next step?
P: 634
Almost there!

 Quote by mindauggas $x_{intercept}$ 0=mx+3-4m >> $-3=m(x-4)$ >> $\frac{-3}{x-4}=m$ (i don't see any way where the variable x would be on the left by itself ... is there one?)
Instead of moving 3 over to the left side, move mx. Then divide both sides by m and you'll find x on the left side.

 $y_{intercept}$ y=3-4m Is this correct? Whats the next step?
This looks perfect.
You figured out the next step in #16, as quoted below:

 Quote by mindauggas So, now I know, that x and y intercept values multiplied amount to 54 (27*2),
 P: 127 $y=3-4m$ $0=mx+3-4m$ $-mx=3-4m$ (dividing by -m) $x=\frac{-3}{m}+4$ $xy=54$, then $(\frac{-3}{m}+4)(3-4m)=54$ $\frac{-9}{m}+4m*\frac{-3}{m}+12-16m=54$ $\frac{-9}{m}-16m=30$ (multiplying by m, we get a quadratic) $16m^{2}+30+9=0$ With the roots -3/2 and -3/8 Awesomenessness ... Thank you very much your patience :)
 P: 634 Right. Now multiply both sides by m. You will arrive at an equation quadratic in m. Solving this will give you the possible values of slope. As a verification, you should check if the sign of the solutions is negative, as SammyS suggested.
 P: 127 Yes ... Solved ... Thank's again :)
 P: 634 No problem

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