Final answer:
The linear function is 6 - (7 - p) / 7 * 5.
Step-by-step explanation:
The linear function that satisfies the conditions f(5) = 7 and f(-2) = p can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we use the formula m = (y2 - y1) / (x2 - x1).
In this case, we have (x1, y1) = (-2, p) and (x2, y2) = (5, 7).
Plugging in the values, we get"
m = (7 - p) / (5 - (-2))
= (7 - p) / 7.
Substituting the point (5, 7) into the equation y = mx + b, we get:
7 = (7 - p) / 7 * 5 + b.
Solving for b, we have b = 6 - (7 - p) / 7 * 5.