Final answer:
The question about the tangent line does not provide enough information, as the function given appears to be a vector. The correct choice is (a) Not enough information provided. To explore a related tangential concept, the slope between two specific points is explained, and the structure of a linear equation is discussed.
Step-by-step explanation:
The student is asking to find the equation of the tangent line for the function f(x)=⟨9,2⟩ at the point x=1. However, the presented function f(x)=⟨9,2⟩ appears to be a vector, not a function, and therefore, the question seems to have missing or incorrect information. Without the correct function, we cannot find a tangent line. Hence, the correct answer to this question would be (a) Not enough information provided.
To further explain a related concept, let's consider the process of finding the slope between two points. Given Point 1: (1, 0.1) and Point 2: (7, 26.8), the slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). Substituting the values, we get m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45, which is approximately 4.5.
Regarding the equation y = 9 + 3x, it represents a straight line where the slope (m) is 3, and the y-intercept (b) is 9. To find specific points on this line, one would simply plug in values for x and solve for y, plotting these points to construct the line graphically.