Final answer:
The lines y=-2x-21 and y=-2/3x-6 do not intersect and therefore, there is no intercept point.
Step-by-step explanation:
The intercept point of the lines y=-2x-21 and y=-2/3x-6 can be found by setting both equations equal to each other:
-2x-21=-2/3x-6
To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction:
-6x-63=-6x-18
Since -6x is equal on both sides, we can add 6x to both sides to isolate the constant terms:
-63=-18
Since -63 does not equal -18, there is no solution to this equation and therefore, the lines y=-2x-21 and y=-2/3x-6 do not intersect. Therefore, there is no intercept point.