Final answer:
The equation of the line perpendicular to the given line of best fit (ŷ = -173.51 + 4.83x) and passing through the point (4, -6) is y = -0.207x - 5.172.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line and passes through a given point, we must first understand the concept of slope in algebra.
The slope of a line measures its steepness and is calculated as the rise over the run (change in y divided by change in x). According to the information provided, the line of best fit is given by the equation ŷ = -173.51 + 4.83x, which means its slope is 4.83. A line that is perpendicular to this one will have a slope that is the negative reciprocal of 4.83, which is approximately -0.207 (rounded to three decimal places).
To find the equation of the perpendicular line, we use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope, (x1, y1) is the point through which the line passes, which in this case is (4, – 6). Substituting the values, we get y - (-6) = -0.207(x - 4). Simplifying, the equation becomes y + 6 = -0.207x + 0.828, and then y = -0.207x + 0.828 - 6. Finally, the equation of the perpendicular line is y = -0.207x - 5.172.