Answer: [tex]y= 1/4x + 20[/tex]
Step-by-step explanation:
To find rate of change, there is an equation. (there is an equation for everything :) ).
The equation is: [tex]y2-y1/x2-x1[/tex]
Now, if you are confused, I am here to explain. Y2 means The y value of the second y point.
In the graph, the second point point is (8,22) (remember, x always comes first!).
Now you need to get the y value, which is 22.
Next, you need to find Y1. The number after y means the point. Y2 means the second point whereas Y1 means the first point.
Y1 = 21 (look at ex. above if needed)
Now you need to find x
Just do the same thing with the y values, but use the x value instead :).
X1= 4
X2= 8
Now you have formed your equation to find the rate of change
22-21/8-4
1/4 is the rate of change.
Or, there is a simpler method called "Rise Over Run".
Basically, you have to see how much the y value rises. Y is the rise, x is the run.
(ex. 21 to 22 (first 2 points) rises 1)
(ex. for X, 4 goes up 4 to get 8)
Now you have two numbers: 1 and 4
Just divide: 1/4 = 1/4 (obviously.)
Now there is also an equation format to help you to form the equation!
That is: [tex]y=mx+b[/tex]
Now, Y is what you are solving for, m is the slope (or rate of change), x is the x value, and b is the y intercept.
So m, the rate of change, is what we have already solved for!
m= 1/4
y=1/4x+b
B is the slope intercept
It is the point that crosses the Y axis.
Which, in this case, is 20.
So, the equation is [tex]y=1/4x +20[/tex]
Hope this helps!
-jp524
