Final answer:
To compare the linear function expressed by the equation y = -x + 3 with the data in the table, substitute the x-coordinate into the equation and check if the resulting y-coordinate matches the given value. If all the coordinates satisfy the equation, then they represent the same function expressed in different ways.
Step-by-step explanation:
To compare the linear function expressed by the equation y = -x + 3 with the data in the table (-4,1)(-2,-1)(1,-4)(3,-6), we need to check if each set of coordinates satisfies the equation. We substitute the x-coordinate into the equation and check if the resulting y-coordinate matches the given value. If all the coordinates satisfy the equation, then they represent the same function expressed in different ways.
Let's substitute the x-coordinate of (-4,1) into the equation: y = -x + 3. Substituting x = -4, we get y = -(-4) + 3, which simplifies to y = 4 + 3, y = 7. Since the y-coordinate of (-4,1) does not match 7, this set of coordinates does not satisfy the equation. We repeat this process for the other three sets of coordinates to determine if they satisfy the equation.
For (-2,-1): y = -x + 3, substituting x = -2, we get y = -(-2) + 3, which simplifies to y = 2 + 3, y = 5. Since the y-coordinate of (-2,-1) matches 5, this set of coordinates satisfies the equation.
For (1,-4): y = -x + 3, substituting x = 1, we get y = -1 + 3, y = 2. Since the y-coordinate of (1,-4) does not match 2, this set of coordinates does not satisfy the equation.
For (3,-6): y = -x + 3, substituting x = 3, we get y = -3 + 3, y = 0. Since the y-coordinate of (3,-6) does not match 0, this set of coordinates does not satisfy the equation. Therefore, the linear function expressed by the equation y = -x + 3 is not the same as the data in the table.