Question

find $\frac{h(8)}{f(-3)}$ in simplified form.
$f(x)$
$g(x) = -x^2 + 3x - 4$

$x$	$h(x)$
$4$	$10$
$-3$	$7$
$8$	$6$
$5$	$9$
$-4$	$-7$

Explanation:

Step1: Find $h(8)$ from table

From the table, when $x=8$, $h(8)=6$.

Step2: Find equation of $f(x)$

The line $f(x)$ passes through $(0,2)$ and $(1,4)$. Slope $m=\frac{4-2}{1-0}=2$. Using $y=mx+b$, $b=2$, so $f(x)=2x+2$.

Step3: Calculate $f(-3)$

Substitute $x=-3$ into $f(x)$:
$f(-3)=2(-3)+2=-6+2=-4$

Step4: Compute the ratio

$\frac{h(8)}{f(-3)}=\frac{6}{-4}$

Step5: Simplify the fraction

$\frac{6}{-4}=-\frac{3}{2}$

Answer:

$-\frac{3}{2}$