Answer:
The linear equation that represent this problem is [tex]y=50x-2,500[/tex]
Step-by-step explanation:
Let
x -----> the number of people
y ----> the profit in dollars
we have
For x=100, y=2,500
and
For x=80, y=1,500
Find the slope m
we have
(80,1,500) and (100,2,500)
The slope is equal to
[tex]m=(2,500-1,500)/(100-80)\\ \\m=50\frac{\$}{people}[/tex]
Find the equation of the line into point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=50[/tex] and point (100,2,500)
substitute
[tex]y-2,500=50(x-100)[/tex] ----> equation in slope point form
Convert to slope intercept form
[tex]y=50x-5,000+2,500[/tex]
[tex]y=50x-2,500[/tex]
