The rate of change of item I is greater than the rate of change of item II. (Option A)
How to find the rate of change of a linear equation?
Suppose that the considered linear equation is of the form [tex]y = mx + c[/tex]
Then, when we change x by 1 unit, then:
[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]
where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.
We found that this change is the value of 'm'.
It is called slope of the line this equation represents (each linear equation represents a line).
Finding rate of each item:
The rate is 3 units increment in y per unit increment in x. In short, the rate is 3 unit / unit increment in x
Since graph of a straight line is given, we can find its slope which would represent its rate.
Consider x = 0, for which y = 0 is given in graph.
Now change x by 1 unit, so x becomes x = 1
At x =1 , y = 2
So we see that as x changes by 1 unit, y goes from 0 to 2 (change of 2 units).
Hence, the rate is 2 units increment in y per unit increment in x. In short, the rate is 2 unit / unit increment in x
Thus, the rate of change of item I is greater than the rate of change of item II. (Option A)
Learn more about rate of change of a function here:
https://brainly.com/question/15125607
