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The diagram below shows part of the graph of y= b-x/ cx+d

The x-intercept is (6,0).
The vertical asymptote is x = -3.
The horizontal asymptote is y = -1.
Find the value of d.

The diagram below shows part of the graph of y= b-x/ cx+d The x-intercept is (6,0). The-example-1
User Wayne Kuo
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Solution

For x-intercept,
y=0


\implies b-x=0


\implies b=6

For vertical intercept
y\rightarrow \pm \infty


\implies cx+d=0


\implies-3x+d=0


\implies d=3c

Now,
y=(6-x)/(cx+3c)


\implies x(xy+1)=6-3cy


\implies x=(6-3xy)/(cy+1)

At horizontal asymptote,
x\rightarrow\pm\infty\implies cy+1=0


\implies c(-1)+1=0


\implies c=1


\implies d=3.

The diagram below shows part of the graph of y= b-x/ cx+d The x-intercept is (6,0). The-example-1
User Kayleigh
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7.8k points