(100 points)
a table of values for function a and the graph of function b are shown. state the slope of function b

state an equation for a third linear function with a rate of change that is between the rates of change for function a and function b.

explain how you know the function you created has a rate of change in between those of function a and function b.

Function A has a slope of (4-(-2))/(4-(-4)) = 6/8 = 3/4, Function B has a slope of 2/5, so any function with a slope between those values will be satisfactory. We know the value 1/2 is between 2/5 and 3/4, so we can make our function have a slope of 1/2.

If we choose a y-intercept of 17/7, then our function will intersect the other two where they already intersect each other. That makes the graph clearly show the rate of change is between the rates of change of the given functions.

A third function that satisfies requirements will be
.. f(x) = (1/2)x +17/7