Question

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.

Answer 1

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`.