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Which of these points lies on the line described by the equation below?

ソー4=ー2（x－6）
• A. (4,6)
• B. (6,4)
O c. (-4, -6)
• D. (-6, -4)

3 answers

To determine which of the given points lies on the line described by the equation \( y = -2(x - 6) \), we first need to simplify the equation.

Starting with the equation given:

\[ y = -2(x - 6) \]

Distributing \(-2\):

\[ y = -2x + 12 \]

Now we can evaluate each point:

  1. Point A: (4, 6) \[ y = -2(4) + 12 = -8 + 12 = 4 \quad \text{(not equal to 6)} \]

  2. Point B: (6, 4) \[ y = -2(6) + 12 = -12 + 12 = 0 \quad \text{(not equal to 4)} \]

  3. Point C: (-4, -6) \[ y = -2(-4) + 12 = 8 + 12 = 20 \quad \text{(not equal to -6)} \]

  4. Point D: (-6, -4) \[ y = -2(-6) + 12 = 12 + 12 = 24 \quad \text{(not equal to -4)} \]

None of the points A, B, C, or D seem to satisfy the equation. However, let's double-check Point B where we previously made a calculation error.

For Point B: (6, 4) \[ y = -2(6) + 12 = 0 \quad \text{(already calculated)} \] However, I realize that I made a logical mistake in interpreting the values. All points need to check against \( y = -2x + 12 \).

Re-evaluating, none of the points meet the equation \( y = -2x + 12 \).

Thus, none of the points \( A, B, C, \) or \( D \) lie on the line described by the initial equation.

U have to pick one tho, the one that is most right

Let's go through the points again carefully with the equation \( y = -2x + 12 \) to find the point that is closest to being correct.

  1. Point A: (4, 6) \[ y = -2(4) + 12 = -8 + 12 = 4 \quad \text{(does not match 6)} \]

  2. Point B: (6, 4) \[ y = -2(6) + 12 = -12 + 12 = 0 \quad \text{(does not match 4)} \]

  3. Point C: (-4, -6) \[ y = -2(-4) + 12 = 8 + 12 = 20 \quad \text{(does not match -6)} \]

  4. Point D: (-6, -4) \[ y = -2(-6) + 12 = 12 + 12 = 24 \quad \text{(does not match -4)} \]

Calculating the predicted \( y \) values for the points gives:

  • For Point A, \( y = 4 \) (actual 6, difference of 2)
  • For Point B, \( y = 0 \) (actual 4, difference of 4)
  • For Point C, \( y = 20 \) (actual -6, difference of 26)
  • For Point D, \( y = 24 \) (actual -4, difference of 28)

The point that is least "off" from the calculated value is Point A (4, 6), with the smallest difference.

So, if I must choose one point that is the most right, I would select:

A. (4, 6)