Take a look at x values and determine if x values are growing/decreasing by a constant

do the same for y values

only if both x and y are growing/decreasing by a constant do you have a linear relationship

for example:

X: 1 2 3 4 5

y: -3 -1 1 3 5

x is increasing by 1 and y is increasing by 2 so it is a linear relationship

however,

x: 1 2 3 4 5

y: 1 2 4 8 10

here x is increasing by 1 by y is growing by a factor of 2 so it is not a linear relationship

do the same for y values

only if both x and y are growing/decreasing by a constant do you have a linear relationship

for example:

X: 1 2 3 4 5

y: -3 -1 1 3 5

x is increasing by 1 and y is increasing by 2 so it is a linear relationship

however,

x: 1 2 3 4 5

y: 1 2 4 8 10

here x is increasing by 1 by y is growing by a factor of 2 so it is not a linear relationship