Final answer:
To determine the value of 'a' for the data in the table to represent a linear function with a rate of change of +5, we need to find the equation of the linear function. None of the given options for 'a' satisfy the requirement for the data to represent a linear function with a rate of change of +5.
Step-by-step explanation:
To determine the value of a for the data in the table to represent a linear function with a rate of change of +5, we need to find the equation of the linear function.
A linear function can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
Since the rate of change is given as +5, the slope (m) will be 5. The equation will be in the form y = 5x + a.
To determine the value of a, we need to look at the table data:
xy3a + 3(5)
From the table, when x = 3, y should be equal to 5(3) + a. This simplifies to 15 + a.
Comparing this to the given options:
- Option 1: a = 3 - not a solution
- Option 2: a = 23 - not a solution
- Option 3: a = 8 - not a solution
- Option 4: a = 18 - not a solution
None of the given options for a satisfy the requirement for the data to represent a linear function with a rate of change of +5. Therefore, the answer is None of the above.