To determine which points are on the line defined by the equation \( y = \frac{2}{1}x + 4 \) (which simplifies to \( y = 2x + 4 \)), we can substitute the x-coordinates of each point into the equation and check if the resulting y-coordinates match those given in the points.
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For the point (6, 4): \[ y = 2(6) + 4 = 12 + 4 = 16 \] The y-coordinate (16) does not match the given y-coordinate (4). So (6, 4) is not on the line.
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For the point (5, 2): \[ y = 2(5) + 4 = 10 + 4 = 14 \] The y-coordinate (14) does not match the given y-coordinate (2). So (5, 2) is not on the line.
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For the point (−4, 2): \[ y = 2(-4) + 4 = -8 + 4 = -4 \] The y-coordinate (-4) does not match the given y-coordinate (2). So (−4, 2) is not on the line.
Based on the calculations, none of the points listed (6, 4), (5, 2), or (−4, 2) lie on the line \( y = 2x + 4 \).