Final answer:
Function A is the linear function, and its equation is y = 1.67x - 0.01.
Step-by-step explanation:
The question relates to determining which of the given functions is linear and finding its equation. Function A presents a set of x and y values that show a consistent rate of change, which suggests that it is indeed a linear function. To confirm this, we can calculate the rate of change (slope) between any two points. Taking the first and second points, (3, 5) and (6, 10), the slope can be calculated as (10 - 5) / (6 - 3) which equals 5 / 3 or 1.67. Since this rate of change or slope is consistent for all points given, the function is linear. Now, to find the equation of the line in the format y = mx + b, we know the slope (m) is 1.67, and to find the y-intercept (b), we can use one of the points. For instance, using the first point (3,5), we can plug the values into the slope-intercept form: 5 = 1.67(3) + b. Solving this gives us b = -0.01. Therefore, to two decimal places, the equation of this linear function is y = 1.67x - 0.01.