Final answer:
The equation of the line using the points (5,12.8) and (45,23.4) is y = 0.265x + 12.475, which does not match any of the given answer choices, suggesting there might be an error in the provided options.
Step-by-step explanation:
To write a linear model using the points (5,12.8) and (45,23.4), we'll first calculate the slope (m) of the line that passes through these points. The formula to calculate the slope is:
m = (y2 - y1) / (x2 - x1)
Substituting the given points into the formula, we get:
m = (23.4 - 12.8) / (45 - 5) = 10.6 / 40 = 0.265
The slope of the line is 0.265. Next, we'll use the slope-intercept form of a linear equation, which is y = mx + b, to find the y-intercept (b). Using one of the given points (5,12.8) with our calculated slope, we get:
12.8 = (0.265)(5) + b
b = 12.8 - (0.265)(5) = 12.475
Therefore, the equation of the line of best fit is y = 0.265x + 12.475. This does not match any of the provided answer choices (A, B, C, D), indicating there may be an error in the question or the answer choices provided.