Final answer:
The line of best fit that passes through the points (0,8) and (4,20) is found using the slope formula and the given points, resulting in the equation y = 3x + 8.
Step-by-step explanation:
The student has asked to find a line of best fit that passes through the points (0,8) and (4,20) when modeling the relationship between total number of points in the game, P, and minutes played, m, for each player in the second half of a game.
To find the equation of the line of best fit, we need two things: a point and the slope. Since we are given two points that the line passes through, we can use these to find the slope.
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are our two points.
Using our points (0,8) and (4,20), we get:
m = (20 - 8) / (4 - 0) = 12 / 4 = 3
Now that we have the slope, we can use one of the points to find the y-intercept (b) of the line equation in the form y = mx + b. Since the line passes through (0,8), where 0 is x and 8 is y, the y-intercept is already given as 8.
Therefore, the equation of the line of best fit is y = 3x + 8.