Answer:
(18,27) , because the rate of change of the function is [tex]\frac{4}{3}[/tex]
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
[tex]m=(7-3)/(3-0)=\frac{4}{3}[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=\frac{4}{3}[/tex]
[tex]b=3[/tex] -----> point (0,3) is the y-intercept
substitute
[tex]y=\frac{4}{3}x+3[/tex]
The rate of change of the linear equation is equal to [tex]\frac{4}{3}[/tex]
Remember that
If a ordered pair is a solution of the linear equation, then the ordered pair must satisfy the linear equation
Verify
1) point (18,27)
substitute the value of x and the value of y in the linear equation
[tex]27=\frac{4}{3}(18)+3[/tex]
[tex]27=24+3[/tex]
[tex]27=27[/tex] -----> 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
[tex]18=\frac{4}{3}(27)+3[/tex]
[tex]18=36+3[/tex]
[tex]18 \neq 39[/tex] -----> 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
