How do you solve Y = 3(b)+4 ?

Question

I have a math question in rate of change and its Y = 3x + 4 

Find the rate of change in y to x in x=a to x=b

So it should be Y = 3(b)+4 but I don't know how to calulate that

Answer 1

The rate of change of a linear equation is the slope, which is 3.  The slope is computed using two points on the line, (a, y_a) and (b, y_b), as follows:

 

m = (y_b-y_a)/(b-a) = (3b+4 - 3a-4)/(b-a) = (3b-3a)/(b-a) = 3(b-a)/(b-a) = 3