Answer:
The slope becomes 0.5625 and y intercept becomes 12.5.
$65.9375
Step-by-step explanation:
Given that
the total reimbursement function in terms of [tex]m[/tex] miles:
[tex]f(x) = 0.45m +5[/tex]
After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.
To find:
How to transform the graph of f.
Total reimbursement for a trip of 95 miles?
Solution:
[tex]f(x) = 0.45m +5[/tex] can also be written as:
[tex]y = 0.45m +5[/tex]
It is nothing but slope intercept form, comparing with [tex]Y = M X+ C[/tex]
M is the slope and C is the y intercept.
Slope of the graph is 0.45.
Y intercept is 5.
After change in the function, first of all add $5.
[tex]0.45m + 5+5 = 0.45m+10[/tex]
Now, multiply with 1.25
Resulting function becomes:
[tex]f(x) =1.25\times (0.45m+10)\\\Rightarrow f(x) =0.5625m+12.5[/tex]
Kindly refer to the attached image for the graph of the two functions.
Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.
To find the reimbursement for a trip of 95 miles:
Put m = 95
[tex]f(95) =0.5625\times 95+12.5 = \bold{\$65.9375 }[/tex]
