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Line slope word problem

by mindauggas
Tags: line, slope, word
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Sourabh N
#19
Feb12-12, 02:50 AM
P: 633
Quote Quote by mindauggas View Post
His equation was: y=mx+3-4m

This becomes:

[itex]y=\frac{3}{4-x}(x)+3-4\frac{3}{4-x}[/itex] (???)

Then [itex]y=\frac{3}{4-x}(x)-1[/itex]

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.
mindauggas
#20
Feb12-12, 03:47 AM
P: 127
Quote Quote by Sourabh N View Post
^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.
[itex]x_{intercept}[/itex] 0=mx+3-4m >> [itex]-3=m(x-4)[/itex] >> [itex]\frac{-3}{x-4}=m[/itex] (i don't see any way where the variable x would be on the left by itself ... is there one?)

[itex]y_{intercept}[/itex] y=3-4m

Is this correct? Whats the next step?
Sourabh N
#21
Feb12-12, 12:41 PM
P: 633
Almost there!

Quote Quote by mindauggas View Post
[itex]x_{intercept}[/itex] 0=mx+3-4m >> [itex]-3=m(x-4)[/itex] >> [itex]\frac{-3}{x-4}=m[/itex] (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.

[itex]y_{intercept}[/itex] 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 Quote by mindauggas View Post
So, now I know, that x and y intercept values multiplied amount to 54 (27*2),
mindauggas
#22
Feb12-12, 01:56 PM
P: 127
[itex]y=3-4m[/itex]

[itex]0=mx+3-4m[/itex]
[itex]-mx=3-4m[/itex] (dividing by -m)
[itex]x=\frac{-3}{m}+4[/itex]

[itex]xy=54[/itex], then

[itex](\frac{-3}{m}+4)(3-4m)=54[/itex]
[itex]\frac{-9}{m}+4m*\frac{-3}{m}+12-16m=54[/itex]
[itex]\frac{-9}{m}-16m=30[/itex] (multiplying by m, we get a quadratic)
[itex]16m^{2}+30+9=0[/itex]
With the roots -3/2 and -3/8

Awesomenessness ... Thank you very much your patience :)
Sourabh N
#23
Feb12-12, 02:07 PM
P: 633
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.
mindauggas
#24
Feb12-12, 02:29 PM
P: 127
Yes ... Solved ... Thank's again :)
Sourabh N
#25
Feb12-12, 02:47 PM
P: 633
No problem


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