Work Step by Step
The x and y-coordinates of all the points on the line $y=x$ are the same. All the points on the line $y=6$ have a y-coordinate of $6$. The line $y=x$ contains the point $(6, 6)$. The line $y=6$ also contains $(6, 6)$. The two lines share the common point $(6, 6)$; therefore their graphs will intersect at $(6, 6)$.