Graph the proportional relationship y = -2x by plotting points.

Question

A. (2, 4), (1, 2), (0, 0)
B. (0, 0), (1, -1), (2, -2)
C. (0, 0), (1, -2), (2, -4)
D. (2, 10), (1, 5), (0, 0)

Answer 1

To graph the proportional relationship $y=-2x$, we need to select points that satisfy this equation.

The equation means that for any $x$, $y$ will be double its negative value. Let's check each option:

A. $(2,4),(1,2),(0,0)$

• For $x=2$: $y=-2(2)=-4$ (not $4$)
• For $x=1$: $y=-2(1)=-2$ (not $2$)
• For $x=0$: $y=-2(0)=0$ (correct)

None of the points in this option satisfy the equation except for $(0,0)$.

B. $(0,0),(1,-1),(2,-2)$

• For $x=0$: $y=-2(0)=0$ (correct)
• For $x=1$: $y=-2(1)=-2$ (not $-1$)
• For $x=2$: $y=-2(2)=-4$ (not $-2$)

Only the first point is correct.

C. $(0,0),(1,-2),(2,-4)$

• For $x=0$: $y=-2(0)=0$ (correct)
• For $x=1$: $y=-2(1)=-2$ (correct)
• For $x=2$: $y=-2(2)=-4$ (correct)

All points satisfy the equation.

D. $(2,10),(1,5),(0,0)$

• For $x=2$: $y=-2(2)=-4$ (not $10$)
• For $x=1$: $y=-2(1)=-2$ (not $5$)
• For $x=0$: $y=-2(0)=0$ (correct)

Only the last point is correct.

Based on the verification, the correct answer is:

C. (0, 0), (1, -2), (2, -4).