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Through which of the following point , t...

Through which of the following point , the graph of y=-x passes?

A

(1,1)

B

(0,1)

C

(-1,1)

D

(0,0)

Text Solution

AI Generated Solution

The correct Answer is:
To determine through which points the graph of the equation \( y = -x \) passes, we can evaluate each given point by substituting the x-coordinate into the equation and checking if the resulting y-coordinate matches. ### Step-by-Step Solution: 1. **Understand the Equation**: The equation \( y = -x \) means that for any value of \( x \), \( y \) will be the negative of that value. This indicates a straight line that passes through the origin (0, 0) and has a slope of -1. 2. **Evaluate Each Point**: We will check each point provided to see if it satisfies the equation \( y = -x \). - **Point 1: (1, 1)** - Substitute \( x = 1 \): \[ y = -1 \] - The point (1, 1) does not satisfy the equation since \( y \) should be -1, not 1. - **Point 2: (0, 1)** - Substitute \( x = 0 \): \[ y = -0 = 0 \] - The point (0, 1) does not satisfy the equation since \( y \) should be 0, not 1. - **Point 3: (-1, 1)** - Substitute \( x = -1 \): \[ y = -(-1) = 1 \] - The point (-1, 1) satisfies the equation since \( y \) is indeed 1 when \( x \) is -1. - **Point 4: (0, 0)** - Substitute \( x = 0 \): \[ y = -0 = 0 \] - The point (0, 0) satisfies the equation since \( y \) is 0 when \( x \) is 0. 3. **Conclusion**: The points through which the graph of \( y = -x \) passes are: - (-1, 1) - (0, 0) ### Final Answer: The graph of \( y = -x \) passes through the points (-1, 1) and (0, 0).
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