Final answer:
The linear function rule for a line passing through the points (2,17) and (8,23) is found by first calculating the slope and then using one of the points to find the y-intercept. The final linear function for this line is y = x + 15.
Step-by-step explanation:
A linear function rule can be written by finding the slope (m) and y-intercept (b) of the line that passes through the given points (2,17) and (8,23). First, calculate the slope:
m = (y2 - y1) / (x2 - x1)
m = (23 - 17) / (8 - 2) = 6 / 6 = 1
Next, use the slope and one of the points to find the y-intercept (b) using the equation y = mx + b, where we replace y with the y-coordinate of the point, x with the x-coordinate, and m with our calculated slope:
17 = 1(2) + b
17 = 2 + b
b = 15
The linear function in terms of x and y for this line is thus y = x + 15.