let the family of lines be 2x+6y=K

this can be written as x/(K/2) +y/(K/6) =1....(intercept form)

which gives the x & y intercept as K/2 & K/6 respectively....

as it is given that the intercept b/w the axes is 10 we can write

K²/4 + K²/36 = 100

it is a quadratic in K so we will get 2 lines.