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In the XY-plane, the line with equation 4x + by + c = 0, where bc 6= 0
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22 Jan 2024, 00:54
22 Jan 2024, 00:54
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In the XY-plane, the line with equation \(4x + by + c = 0\), where \(bc \neq 0\), has slope \(\frac{2}{3}\). What is the value of b?
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Re: In the XY-plane, the line with equation 4x + by + c = 0, where bc 6= 0
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22 Jan 2024, 11:47
22 Jan 2024, 11:47
1
Start with the given equation, \(4x + by + c = 0\).
Move x and c to the right to only have y on the left (slope intercept form: y = mx+b, where m is the slope).
\(by = -4x - c\)
\(y = -\frac{4}{b}x - \frac{c}{b}\)
Now we see that m = \(-\frac{4}{b}\). Set it equal to the given slope, \(\frac{2}{3}\)
\(\frac{2}{3} = -\frac{4}{b}\)
Cross multiply the fractions.
\(2*b = -3*4\)
\(b = -6\)
Move x and c to the right to only have y on the left (slope intercept form: y = mx+b, where m is the slope).
\(by = -4x - c\)
\(y = -\frac{4}{b}x - \frac{c}{b}\)
Now we see that m = \(-\frac{4}{b}\). Set it equal to the given slope, \(\frac{2}{3}\)
\(\frac{2}{3} = -\frac{4}{b}\)
Cross multiply the fractions.
\(2*b = -3*4\)
\(b = -6\)
gmatclubot
Re: In the XY-plane, the line with equation 4x + by + c = 0, where bc 6= 0 [#permalink]
22 Jan 2024, 11:47
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