in this problem, we have the ordered pairs
(-2,0) and (6,6)
Let
t=0 hours (midnight)
Find out the equation
step 1
Find out the slope
m=(6-0)/(6+2)
m=6/8
simplify
m=3/4
step 2
Find out the equation in slope-intercept form
H=mt+b
we have
m=3/4
point (6,6)
substitute and solve for b
6=(3/4)(6)+b
6=(18/4)+b
b=6-(18/4)
b=6/4=3/2
therefore
H=(3/4)t+(3/2)
or
H=0.75t+1.5
Part c
For t=5 hours
substitute
H=0.75(5)+1.5
H=5.25 m
Part d
For H=4 m
substitute
4=0.75t+1.5
solve for t
0.75t=4-1.5
0.75t=2.5
t=3.33 hours---------> 3 1/3 hours=3 hours 20 min
therefore
the time is
00:00+3 h 20 min=3:20 am
Part a
Find out the graph
using a graphing tool