To determine whether the point (6, 1850) is on the line represented by the instructor's savings and expenses, we first need to establish the equation of the line based on the given information.
-
Identify the variables:
- Let's denote
as the number of months and as the amount of money saved after months. - The instructor starts with $3,500 and pays $275 each month.
- Let's denote
-
Formulate the equation:
- The amount of savings after
months can be represented by the equation: - This equation indicates that starting from an initial amount of $3,500, the instructor's savings decrease by $275 for every month (x).
- The amount of savings after
-
Check if the point (6, 1850) lies on the line:
- Substitute
into the equation to find : - Compute
: - Now, calculate
:
- Substitute
-
Conclusion:
- The calculated
value when is 1850. - Therefore, the point (6, 1850) lies on the line described by the equation
, and the instructor is indeed correct.
- The calculated
How to Check if a Point is on a Line:
To check if a point
- Substitute
(the x-coordinate of the point) into the equation to calculate . - Compare the calculated value
with (the y-coordinate of the point). - If
, then the point lies on the line. - If
, then the point does not lie on the line.