The table of values shown below represents a linear function. Which of these points could also be an ordered pair in the table, andwhy?

Answer:(18,27) , because the rate of change of the function is [tex]\frac{4}{3}[/tex]Step-by-step explanation:step 1Find the slope of the linear equationLooking at the tablewe have the points (0,3) and (3,7)The slope is equal to[tex]m=(7-3)/(3-0)=\frac{4}{3}[/tex]step 2Find the equation of the line in slope intercept form[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptwe have[tex]m=\frac{4}{3}[/tex][tex]b=3[/tex] -----> point (0,3) is the y-interceptsubstitute[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 thatIf a ordered pair is a solution of the linear equation, then the ordered pair must satisfy the linear equationVerify 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 truesoThe ordered pair is a solution of the linear equationthereforeThe point (18,27) could also be an ordered pair in the table2) 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 truesoThe ordered pair is not a solution of the linear equationthereforeThe point (27,18) could not be an ordered pair in the table