Answer:
k = 7
Explanation:
You want to know the value of k that transforms f(x) = 2/3x -3 to g(x) = f(x) +k, where g(x) is 2/3x +4.
Vertical shift
The amount of vertical shift to get from f(x) to g(x) can be found by subtracting f(x) from g(x):
g(x) = f(x) +k
g(x) -f(x) = k
(2/3x +4) -(2/3x -3) = k
4 -(-3) = k = 7
Function f(x) is shifted upward by k = 7 to transform it to g(x).
__
Additional comment
We can read the equations from the graph by looking for the y-intercept (b) and the slope (m = rise/run) of each line. The slope is rise=-2 for run=3, so m=-2/3.
The +k means the transformation is a vertical shift. You don't need to know what the equations for f(x) and g(x) are; you only need to look at the difference between the y-intercepts. That difference is the amount by which g(x) is shifted upward.