Final answer:
The rule for the given data set is a linear function with a slope of 2.5 and a y-intercept of 2, resulting in the equation y = 2.5x + 2.
Step-by-step explanation:
The question requires us to find the rule, or mathematical function, that describes the relationship between the values of x and y in a given data set. From the data points (x, y) = (2, 7), (4, 12), and (6, 17), we can observe that as x increases by 2, y increases by 5. This suggests a linear relationship, so we can write the equation of the line as y = mx + b, where m is the slope and b is the y-intercept.
To find m (the slope), we can use two data points: (2, 7) and (4, 12). The slope m = (y2 - y1) / (x2 - x1) = (12 - 7) / (4 - 2) = 5 / 2 = 2.5. To find the y-intercept b, we can substitute one of the points into the equation along with our slope: 7 = 2.5(2) + b, solving for b gives us b = 2. Using these values, the equation of the line is y = 2.5x + 2.