Answer:
(18,27) , because the rate of change of the function is ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Step-by-step explanation:
step 1
Find the slope of the linear equation
Looking at the table
we have the points (0,3) and (3,7)
The slope is equal to
![m=(7-3)/(3-0)=\frac{4}{3}](https://tex.z-dn.net/?f=m%3D%287-3%29%2F%283-0%29%3D%5Cfrac%7B4%7D%7B3%7D)
step 2
Find the equation of the line in slope intercept form
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope
b is the y-intercept
we have
![m=\frac{4}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4%7D%7B3%7D)
-----> point (0,3) is the y-intercept
substitute
![y=\frac{4}{3}x+3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B4%7D%7B3%7Dx%2B3)
The rate of change of the linear equation is equal to ![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Remember that
If a ordered pair is a solution of the linear equation, then the ordered pair must satisfy the linear equation
<u><em>Verify </em></u>
1) point (18,27)
substitute the value of x and the value of y in the linear equation
![27=\frac{4}{3}(18)+3](https://tex.z-dn.net/?f=27%3D%5Cfrac%7B4%7D%7B3%7D%2818%29%2B3)
![27=24+3](https://tex.z-dn.net/?f=27%3D24%2B3)
-----> is true
so
The ordered pair is a solution of the linear equation
therefore
The point (18,27) could also be an ordered pair in the table
2) point (27,18)
substitute the value of x and the value of y in the linear equation
![18=\frac{4}{3}(27)+3](https://tex.z-dn.net/?f=18%3D%5Cfrac%7B4%7D%7B3%7D%2827%29%2B3)
![18=36+3](https://tex.z-dn.net/?f=18%3D36%2B3)
-----> is not true
so
The ordered pair is not a solution of the linear equation
therefore
The point (27,18) could not be an ordered pair in the table