Find the rate of change for the numbers shown below. Express number as a fraction.
(-3,7)
(0,5)
(3,3)
(6,1)
(5-7)/(0-(-3)) = -2/3
(3-5)/(3-0) = -2/3 remarkable
(1-3)/(6-3) = -2/3
just for sport
(1-7)/(6-(-3)) = -6/9 = -2/3 how do you like that? It might be a straight line through those points with slope = -2/3
Try one of those points in
y = -(2/3)x + b
7 = (-2/3)(-3) + b
7 = 2+b
b = 5
so
y = -(2/3) x + 5 goes through all points I believe
Try it in the last point
1 = -(2/3)(6) + 5 ?
1 = -4 + 5
1 = 1 , sure enough, done
If you followed that, you can do them all without my help.
To find the rate of change for the numbers given, we can calculate the difference in the y-values divided by the difference in the x-values. This will give us the slope or rate of change.
Let's calculate the rate of change between the points (-3,7) and (0,5).
The difference in the y-values is 5 - 7 = -2.
The difference in the x-values is 0 - (-3) = 3.
The rate of change is (-2) / 3.
So, the rate of change for the first two points is -2/3.
Now, let's calculate the rate of change between the points (0,5) and (3,3).
The difference in the y-values is 3 - 5 = -2.
The difference in the x-values is 3 - 0 = 3.
The rate of change is (-2) / 3.
So, the rate of change for the second two points is also -2/3.
Lastly, let's calculate the rate of change between the points (3,3) and (6,1).
The difference in the y-values is 1 - 3 = -2.
The difference in the x-values is 6 - 3 = 3.
The rate of change is (-2) / 3.
So, the rate of change for the last two points is once again -2/3.
Therefore, the rate of change for all the given points is -2/3.