To estimate the line of best fit using the two points (2, 8) and (8, 5), we first need to calculate the slope of the line connecting these points. The formula for slope (m) is:
m = (y2 – y1) / (x2 – x1)
Here, (x1, y1) = (2, 8) and (x2, y2) = (8, 5).
Substituting in the values:
m = (5 – 8) / (8 – 2) = -3 / 6 = -1/2
Next, we can use the slope-intercept form of a line, which is: y = mx + b, where b is the y-intercept.
To find b, we can use one of the points. Let’s use (2, 8):
8 = (-1/2)(2) + b
Now solving for b:
8 = -1 + b
b = 8 + 1 = 9
Now we have both m and b. Therefore, the equation of the line of best fit is:
y = -1/2x + 9
This line represents the best fit through the two points given.