Final answer:
To write a linear function rule for a set of data points that do not align perfectly, a line of best fit is calculated using regression analysis, resulting in an equation of the form y = mx + b.
Step-by-step explanation:
The goal is to write a linear function rule for the given set of data points: (0,3), (1,4), (2,-1), (3,-3), (4,-5). To find the linear equation of the form y = mx + b, where m is the slope and b is the y-intercept, we can use the slope formula m = (y2 - y1) / (x2 - x1) and calculate it between any two points.
However, because the given points do not lie on a straight line, there is no true linear function that perfectly fits all points. Instead, we can calculate the line of best fit, often through a method like least squares regression, which might not pass exactly through any of the points but provides the best approximation of the data's trend.
Using a calculator or computer software that can perform regression analysis, such as a graphing calculator, spreadsheet software, or statistical software, we can input the data points and find the linear regression equation.
For example, we might end with an equation like y = mx + b, with specific values for m and b rounded to four decimal places.