Part A) Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480. Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days
Let
x-------> the number of days
y------> the total rent
A------> point (2,225)
B------> point (5,480)
Step 1
Find the slope AB
[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]
[tex] mAB=\frac{(480-225)}{(5-2)} [/tex]
[tex] mAB=\frac{(255)}{(3)} [/tex]
[tex] mAB=85 [/tex]
Step 2
with m=[tex] 85 [/tex] and the point A Find the equation of the line
[tex] y-y1=m*(x-x1) [/tex]
[tex] y-225=85*(x-2) [/tex]
[tex] y=85x-170+225 [/tex]
[tex] y=85x+55 [/tex]
we know that
the equation of the line in the standard form is equal to
[tex] Ax+By=C [/tex]
so
[tex] -85x+y=55 [/tex]
therefore
the answer part 1) is
[tex] -85x+y=55 [/tex]
Part 2)Write the equation obtained in Part A using function notation
[tex] f(x)=85x+55 [/tex]
the answer Part 2) is
[tex] f(x)=85x+55 [/tex]
Part 3)Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.
Graph the equation by striking a line through the points [tex] (2,225) [/tex] and [tex] (5,480) [/tex]
using a graph tool
see the attached figure
