Function 1: y = 4x + 5 function 2: the line passing through the points (1, 6) and (3, 10). which of these functions has the greater rate of chang

function 1

Rate of change of function 1:
Following the format of y=mx+c, the rate of change should be m, so, the rate of change for function 1 = 4

To find the gradient (rate of change):
The two points the line passes through are (x1, y1) and (x2, y2), which in this case is (1, 6) and (3, 10)
(Doesn't matter which is which but you need to make sure that once you decide which is which, you stick to it)
To calculate the gradient, you substitute these values following (y1 - y2)/(x1 - x2)

Gradient of function 2 = (10 - 6)/(3 - 1)
= 2

Therefore, since 4 > 2, rate of change of function 1 > rate of change of function 2.

The correct answer for this question is this one:

The large image has a scale of 2.5.
The small image has a scale of 0.5

The scale factor that was applied to the first rectangle to get the resulting image is 
= 2.5 / 0.5
= 5
Hope this helps answer your question and have a nice day ahead.