Final answer:
After testing the given x values in the provided equations, it's apparent that only the equation y = -3x + 1 consistently matches the y values in the table for every x value. Therefore, the equation that accurately represents the relationship between the x and y values given in the table is y = -3x + 1.
Step-by-step explanation:
To determine which equation accurately represents the relationship between the x and y values given in the table, we need to test each of the options provided to see if they fit the data points.
Let's compute the values of y using each equation with the given x values:
- For the equation y = x + 9, when x = -2, y = -2 + 9 = 7.
- For the equation y = x² + 3, when x = -2, y = (-2)² + 3 = 4 + 3 = 7.
- For the equation y = -3x + 1, when x = -2, y = -3(-2) + 1 = 6 + 1 = 7.
- For the equation y = x - 7, when x = -2, y = -2 - 7 = -9.
However, only one equation will fit all points. Calculating further and checking other x values, we find that:
- For A) y = x + 9, at x = 10, y should be 10 + 9 = 19, but in the table y = -29.
- For B) y = x² + 3, the square term indicates it's not linear.
- For C) y = -3x + 1, when x = 2, y should be -3(2) + 1 = -5, which matches the table.
- For D) y = x - 7, the previous mismatch rules it out.
Comparing all the points from the table with the results obtained using equation C, we see that it consistently produces the correct y values. Therefore, the correct equation is y = -3x + 1.