Final answer:
To find the value of f(-3) for a linear function, we calculate the slope (m) from the given values f(2) = 9 and f(-2) = 7, which is 0.5. Then we find the y-intercept (b) using one of the points to get the linear equation y = 0.5x + 8. Using this equation, we calculate f(-3) to be 6.5.
Step-by-step explanation:
To find the value of f(-3) for a linear function given that f(2) = 9 and f(-2) = 7, we first need to determine the slope of the line and then use this information to find our desired value.
The slope (m) of a linear function is the change in the function's values divided by the change in the input values. Therefore, the slope can be calculated as follows:
m = (f(2) - f(-2)) / (2 - (-2))
= (9 - 7) / (2 + 2)
= 2 / 4
= 0.5
Now that we have the slope, we can use one of the given points to find the y-intercept (b). Let's use the point (2,9).
9 = 0.5(2) + b
9 = 1 + b
b = 9 - 1
b = 8
Therefore, the linear equation can be expressed as y = 0.5x + 8. Now we can find f(-3).
f(-3) = 0.5(-3) + 8
= -1.5 + 8
= 6.5
The value of f(-3) is 6.5.