To determine which point lies on the line described by the equation [tex]\( y = x \)[/tex], we need to ensure that the coordinates of the point satisfy this equation. Let's go through each option step by step:
1. Option A: (6, -6)
- Here, the x-coordinate is 6 and the y-coordinate is -6.
- Substituting these into the equation [tex]\( y = x \)[/tex], we get:
[tex]\[
-6 \neq 6
\][/tex]
- Therefore, this point does not lie on the line.
2. Option B: (6, 0)
- Here, the x-coordinate is 6 and the y-coordinate is 0.
- Substituting these into the equation [tex]\( y = x \)[/tex], we get:
[tex]\[
0 \neq 6
\][/tex]
- Therefore, this point does not lie on the line.
3. Option C: (-6, 2)
- Here, the x-coordinate is -6 and the y-coordinate is 2.
- Substituting these into the equation [tex]\( y = x \)[/tex], we get:
[tex]\[
2 \neq -6
\][/tex]
- Therefore, this point does not lie on the line.
4. Option D: (-6, -6)
- Here, the x-coordinate is -6 and the y-coordinate is -6.
- Substituting these into the equation [tex]\( y = x \)[/tex], we get:
[tex]\[
-6 = -6
\][/tex]
- This satisfies the equation [tex]\( y = x \)[/tex].
Since only the coordinates [tex]\( (-6, -6) \)[/tex] satisfy the line equation [tex]\( y = x \)[/tex], we conclude that the correct answer is:
Option D: (-6, -6)
