Estimate the line of best fit using two points on the line (2 8) (8 5).

a) y = (1/2)x + 9

b)  y = - (1/2)x + 9

c)  y = 2x + 9

d) y =  -2x + 9

A line is a figure formed when two points are connected with minimum distance between them, and both the ends extended to infinity.

Answer: The line of best fit using two points on the line (2 8) (8 5) is option (b) y = -(1/2)x +9

Let's look into the solution

Explanation:

Put the values of x and y coordinates in the given equations:

The points given are (2,8) (8,5)

Let's take option (A) : y = (1/2)x + 9

1) For (2,8), let x = 2 and y = 8

LHS: 8

RHS: (1/2)x + 9

⇒ (1/2) × 2 + 9 = 10      

8 ≠ 10

LHS ≠ RHS

Let's take option (B) : y = - (1/2)x + 9

1) For (2,8), let x = 2 and y = 8

LHS: 8

RHS: - (1/2)x + 9

⇒ - (1/2) × 2 + 9 = 8    

⇒ 8 = 8 (LHS = RHS)

2) For (8,5), let x = 8 and y = 5

LHS: 5

RHS: - (1/2)x + 9

⇒ - (1/2) × 8 + 9 = 5   

⇒ 5 = 5 (LHS = RHS)

Thus, the line of best fit using two points on the line (2 8) (8 5) is an option (b) y = -(1/2)x +9.