Answer: 9.5
Explanation:
a. To find the equation that represents the linear function f, we need to first find the slope (m) between the two points and use the point-slope form of a linear equation:
y = m(x - x1) + y1
where x1 and y1 are the coordinates of one of the two points.
The two points are (3, 2) and (9, 9).
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values from the two points:
m = (9 - 2) / (9 - 3) = 7 / 6
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation that represents f:
y = m(x - x1) + y1
y = (7/6)(x - 3) + 2
b. To find f(6), we need to plug in 6 for x into the equation for f:
y = (7/6)(6 - 3) + 2
y = (7/6)(3) + 2
y = (7/6) * 3 + 2
y = 7/2 + 2
y = 9.5
So, f(6) = 9.5.