A linear function has highest power (exponent) of a variable as 1.
Option 1) 2x+5y=13 : Power of x and y are 1 there, so it's a linear function.
Option 2) -x^3 =3y+10 : Power of y is 1 but power of x is 3, so it's not a linear function.
Option 3) 3(2x^4+y)=14 :Power of y is 1 but power of x is 4, so it's not a linear function.
Option 4) y=13-2x^2 : Power of y is 1 but power of x is 2, so it's not a linear function.
Option 5) 2=y+x^5 : Power of y is 1 but power of x is 5, so it's not a linear function.
Option 6) y=x+7 :Power of x and y are 1 there, so it's a linear function.
Therefore, only functions 2x+5y=13 and y=x+7 are linear functions.
