In the xy-coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y – 7, then k = ?

Points (a, b) and [(a + 3), (b + k)] will satisfy

the equation

x – 3y + 7 = 0.

∴ a – 3b + 7 = 0 .......(i)

and a + 3 – 3 (b +k) + 7 = 0

$Rightarrow a+3-3 b-3 k+7=0$

$Rightarrow a-3 b+7+3-3 k=0$

$Rightarrow 3-3 k=0 Rightarrow 3 k=3$

$Rightarrow k=frac{3}{3}=1[ecause a-3 b+7=0]$