Answer
(a) slope=5
(b) Increase in the quantity of tomatoes harvested is 5 hundred pounds per inch increase in rainfall
(c) The quantity of tomatoes harvested 600 pounds when rainfall is zero inches
Work Step by Step
(a)
$f(x)=5x+6=mx+c$
where m is the slope
$\Longrightarrow$
m=slope=5
(b)
$\delta f(x)$=f(x+$\delta x$)-f(x)
$\delta f(x)$=f(x+$\delta x$)-f(x)
$\delta f(x)$=5(x+$\delta x$)+6-(5x+6 )
$\delta f(x)$=5x+5$\delta x$+6-5x-6
$\delta f(x)$=5$\delta x$
$\frac{ \delta f(x)}{ \delta x}=5$
$\Longrightarrow$
Increase in the quantity of tomatoes harvested is 5 hundred pounds/increase in rainfall in inches.
Increase in the quantity of tomatoes harvested is 5 hundred pounds per inches increase in rainfall
(c)
Put x=0 in
$f(0)=5\times 0+6=6$
The quantity of tomatoes harvested 600 pounds when rain fall is zero inches
