To determine which points satisfy the equation \( 2x + y = 6 \), we can substitute the \( x \) and \( y \) values from each point into the equation and check if it holds true.
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For the point \( (6, 2) \): \[ 2(6) + 2 = 12 + 2 = 14 \quad \text{(not a solution)} \]
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For the point \( (-2, 2) \): \[ 2(-2) + 2 = -4 + 2 = -2 \quad \text{(not a solution)} \]
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For the point \( (4, -2) \): \[ 2(4) + (-2) = 8 - 2 = 6 \quad \text{(solution)} \]
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For the point \( (0, 6) \): \[ 2(0) + 6 = 0 + 6 = 6 \quad \text{(solution)} \]
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For the point \( (5, -8) \): \[ 2(5) + (-8) = 10 - 8 = 2 \quad \text{(not a solution)} \]
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For the point \( (6, -6) \): \[ 2(6) + (-6) = 12 - 6 = 6 \quad \text{(solution)} \]
The points that are solutions to the equation \( 2x + y = 6 \) are \( (4, -2) \), \( (0, 6) \), and \( (6, -6) \).
Plotting the Points
- (4, -2)
- (0, 6)
- (6, -6)
Equation of the Line
To draw the line through these points, we can express the equation in slope-intercept form \( y = mx + b \). The equation \( 2x + y = 6 \) can be rewritten as: \[ y = -2x + 6 \] Where the slope \( m = -2 \) and the y-intercept \( b = 6 \).
Summary
The three points that are solutions to the equation \( 2x + y = 6 \) are:
- \( (4, -2) \)
- \( (0, 6) \)
- \( (6, -6) \)
After plotting these points and drawing the line, you'll clearly see they all lie on the line \( y = -2x + 6 \).