To determine which points are on the line described by the equation \( y = -4x \), we can substitute the \( x \) values of the given points into the equation and see if they yield the corresponding \( y \) values.
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For the point \( (-2, 8) \): \[ y = -4(-2) = 8 \] This point satisfies the equation.
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For the point \( (-12, 3) \): \[ y = -4(-12) = 48 \] This point does not satisfy the equation.
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For the point \( (0, 0) \): \[ y = -4(0) = 0 \] This point satisfies the equation.
Now, we can summarize the results:
- The point \( (-2, 8) \) is on the line.
- The point \( (-12, 3) \) is not on the line.
- The point \( (0, 0) \) is on the line.
Thus, the points that are on the line \( y = -4x \) are \( (-2, 8) \) and \( (0, 0) \).
Based on the options given, the correct answer is Two of these.