3/2 I'm pretty sure idk if I'm right though but you'll do good!
first off, is noteworthy that's the graph of an exponential function, thus the function will be along the lines of g(x) = abˣ , now, what's "a" and "b" values?
well, let's take a peek when x = 0 and x = 1.
![\bf g(x) = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 0\\ y = 1 \end{cases}\implies 1=ab^0\implies 1=a(1)\implies \boxed{1=a} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 1\\ y = 4 \end{cases}\implies 4 = ab^1\implies 4=1b^1\implies \boxed{4=b} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill g(x) = 4^x\qquad \qquad \qquad \begin{array}{|c|c|ll} \cline{1-2} x&y\\ \cline{1-2} -2&\frac{1}{4^2}\to \frac{1}{16}\\ -1&\frac{1}{4}\\ 0&1\\ 1&4\\ 2&16\\ \cline{1-2} \end{array}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20g%28x%29%20%3D%20ab%5Ex%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20x%20%3D%200%5C%5C%20y%20%3D%201%20%5Cend%7Bcases%7D%5Cimplies%201%3Dab%5E0%5Cimplies%201%3Da%281%29%5Cimplies%20%5Cboxed%7B1%3Da%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20x%20%3D%201%5C%5C%20y%20%3D%204%20%5Cend%7Bcases%7D%5Cimplies%204%20%3D%20ab%5E1%5Cimplies%204%3D1b%5E1%5Cimplies%20%5Cboxed%7B4%3Db%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20g%28x%29%20%3D%204%5Ex%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cll%7D%20%5Ccline%7B1-2%7D%20x%26y%5C%5C%20%5Ccline%7B1-2%7D%20-2%26%5Cfrac%7B1%7D%7B4%5E2%7D%5Cto%20%5Cfrac%7B1%7D%7B16%7D%5C%5C%20-1%26%5Cfrac%7B1%7D%7B4%7D%5C%5C%200%261%5C%5C%201%264%5C%5C%202%2616%5C%5C%20%5Ccline%7B1-2%7D%20%5Cend%7Barray%7D~%5Chfill)
Answer:
4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 7 ← is in slope- intercept form
with slope m = 4
For a linear function the slope is the measure of it's rate of change.
Thus rate of change is 4