Which best compares the slopes and y-intercepts of the linear functions f and g, where f=1/3+3 and g is shown in the table above? a. the slope of f is less than the slope of g. the y- intercept of f is greater than the y- intercept of g. b. the slope of f is greater than the slope of g. the y-intercept of f is the same as the y-intercept of g. c. the slope of f is the same as the slope of g. the y-intercept of f is less than the y-intercept of g. d. the slope of f is less than the slope of g. the y- intercept of f is the same as the y-intercept of g.

D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is the same as the y-intercept of g(x).

The easiest way to solve this problem is using the slope equation m = y₂ - y₁/x₂ - x1.

From the table we can see while x increases one unit, g(x) increases three unit. Then, this table represent a straight line define by g(x) = mx + b where m is the slope, and b is the y-intercept when x = 0.

m = 6 - 3/1 - 0 = 3/1 = 3

From the table in the image when x = 0 g(x) = y = 3

Writing with the form y = g(x) = mx + b

g(x) = 3x + 3

Analyzing the equation f(x) = 1/3x + 3 and g(x) = 3x + 3, we can see that the slope of f(x) is less than the slope of g(x), and the y-intercept of f(x) is the same than the y-intercept of g(x).