Respuesta :
Find a function that describes the expenses on Nick's vacations using the given information.
Use the number of days as the variable x and the expenses as the variable y.
According to the statement, 2 of the points in the function must be (5, 550) and (9, 950).
Find the slope of the line:
[tex]m=\frac{950-550}{9-5}=\frac{400}{4}=100[/tex]Now, use this slope and one of the given points in the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-550=100(x-5) \\ y=100x-500+550 \\ y=100x+50 \end{gathered}[/tex]This is the equation that describes the relationship between the days and the expenses on Nick's vacation.
The last step is to replace y for 2250 and solve for x, this way, you find the number of days he can be on his vacations with the way he is spending.
[tex]\begin{gathered} 2250=100x+50 \\ 2250-50=100x \\ 2200=100x \\ \frac{2200}{100}=x \\ 22=x \\ x=22 \end{gathered}[/tex]He can be 22 days on vacation with the way he is spending.
