Question

$f$ is a linear function. Values of $x$ and $f\left(x\right)$ are given in the table; complete the table

$x$	$f\left(x\right)$
$-3$	$17$
$0$	--
--	$1$
$4$	$-18$
$7$	--
--	$-30$

Answer 1

$f$ is a linear function

$mx+c$ is linear equation.

when $x=-3$

$f\left(x\right)=17$

$f\left(x\right)=mx+c$

$17=-3m+c-----------\left(1\right)$

when $x=4$

$f\left(x\right)=-18$

$-18=4m+c--------------\left(2\right)$

Solving equation $\left(1\right)and\left(2\right)$

$m=-5$

Put m=-5 in equation(1)

$17=-3m+c$

$c=2$

when $x=0$

$f\left(x\right)=m\times 0+2$

$f\left(x\right)=2$

when$f\left(x\right)=1$

$1=-5x+2$

$x=\frac{1}{5}$

when $x=7$

$f\left(x\right)=7\times -5+2$

$f\left(x\right)=33$

when, $f\left(x\right)=-30$

$-30=-5\times x+2$

$x=\frac{32}{5}$

$x$	$f\left(x\right)$
$-3$	$17$
$0$	$2$
$\frac{1}{5}$	$1$
$7$	$-33$
$\frac{32}{5}$	$-30$