Question 88342
Find the value of k so that the given line has the given slope.
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#5.   (k+5)x + 6y = 42;  m=4/3 
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(k+5)x + 6y = 42 is in the standard form
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Put equation into the slope/intercept form
6y = -(k+5)x + 42
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y = {{{(-(k+5)x)/6}}} + {{{42/6)}}}
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y = {{{(-(k+5)x)/6}}} + 7
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That makes {{{(-(k+5))/6}}}} the slope, the problem said the slope was 4/3; therefore:
{{{(-(k+5))/6}}} = {{{4/3}}}
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Multiply the equation by 6 and you have:
-(k+5) = 4(2)
-(k+5) = 8
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Mult equation by -1, you have:
k + 5 = -8
k = -8 - 5
k = -13
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Check our solution. Substitute for k in the original equation:
(-13+5)x + 6y = 42
-8x + 6y = 42
6y = +8x + 42
y = {{{8/6}}}x + {{{42/6}}}
y = {{{4/3}}}x + 7; m = 4/3 as required
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Did this make sense?