Answer
a) $f(x)=-\dfrac{3}{4}x-5$
b) See graph
Work Step by Step
We are given the linear function:
$f(0)=-5$
$f(4)=-8$
a) The function passes through the points:
$(0,-5)$
$(4,-8)$
Determine the slope of the line:
$m=\dfrac{-8-(-5)}{4-0}=\dfrac{-3}{4}=-\dfrac{3}{4}$
Determine the equation of the line using the slope and one of the points:
$y-(-5)=-\dfrac{3}{4}(x-0)$
$y+5=-\dfrac{3}{4}x$
$y=-\dfrac{3}{4}x-5$
$f(x)=-\dfrac{3}{4}x-5$
b) Use the two points to graph the line:
