Question

Please help now. I’m very confused and i don’t no how to do this. I don’t want just the answer but a great explanation.

Answer 1

First option

Explanation:

Hi there!

The "constant additive rate of change" means a constant slope.

The slope is
`\displaystyle\frac{change \hspace{4} in \hspace{4} y}{change \hspace{4} in \hspace{4} x}`.

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
`-\displaystyle (1)/(4)`. 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!