Question

If $f\left(x\right)=ax+b,$ where, a and b are integers, $f(-1)=-5$ and $f\left(3\right)=3,$ then a and b are equal
(a) $a=-3,b=-1$
(b) $a=2,b=-3$
(c) $a=0,b=2$
(d) $a=2,b=3$

Answer 1

The correct option is $\left(b\right):a=2,b=-3$

Given, $f\left(x\right)=ax+b$

$f(-1)=-5$ [Given]

$\Rightarrow a(-1)+b=-5$

$\Rightarrow -a+b=-5\dots \dots \left(i\right)$

And, $f\left(3\right)=3$ [Given]

$\Rightarrow 3a+b=3\dots \dots \left(ii\right)$

On subtracting eq.(i) from (ii), we get

$3a+b-(-a+b)=3+5$

$\Rightarrow 3a+b+a-b=8$

$\Rightarrow a=2$

On putting $a=2$ in $eq.\left(i\right),$ we get

$-2+b=-5$

$\Rightarrow b=-5+2=-3$