Answer:
First option
Step-by-step explanation:
Hi there!
The "constant additive rate of change" means a constant slope.
The slope is [tex]\displaystyle\frac{change \hspace{4} in \hspace{4} y}{change \hspace{4} in \hspace{4} x}[/tex].
First of all, if the slope is constant, then we know immediately that it must be a linear function, a line. The change in y is forever the same according to the change in x. Knowing this, the second option is for-sure wrong (it's not a straight line).
Now, let's look at the first option. It is a linear function, which means it has a constant slope. However, we're given that the slope is [tex]-\displaystyle \frac{1}{4}[/tex]. This means that for a line, whenever it travels 4 units to the right, it travels 1 unit down (it travels down whenever the slope is negative and up whenever the slope is positive).
This is the exact case for the first option. Look at the point (-2,2) on the line. When we move 4 units to the right of that point, The line would have moved 1 unit down. We would reach the point (2,1).
Therefore, the correct answer would be the first option.
I hope this helps!
