Let's analyze the given linear function [tex]\( h(x) = -\frac{2}{3} x + 5 \)[/tex].
To understand how to move the graph down by 3 units, let's focus on the part of the equation that is responsible for shifting the graph vertically. This part is the constant term, [tex]\( b \)[/tex], which in this case is 5.
When you change the value of [tex]\( b \)[/tex], it affects the vertical position of the graph without affecting its slope.
To move the graph down by 3 units, we need to subtract 3 from the current value of [tex]\( b \)[/tex]:
[tex]\[ b = 5 - 3 = 2 \][/tex]
So, the new equation of the function after this change becomes:
[tex]\[ h(x) = -\frac{2}{3} x + 2 \][/tex]
This modifies the vertical position of the graph by shifting it downward by 3 units.
Therefore, the correct change to move the graph down by 3 units is to change [tex]\( b \)[/tex] to 2. This means the correct answer is:
- The value of [tex]\( b \)[/tex] to 2
