Which equation gives the rule for the table?

Understand the Problem

The question asks to identify the equation that correctly relates the x and y values provided in the table. We need to determine which of the given equations holds true for all pairs of (x, y) in the table.

Answer

$y = x - 3$

Steps to Solve

Test the first equation $y = 3x - 3$ with the first point (3, 0)

Substitute $x = 3$ into the equation: $y = 3(3) - 3 = 9 - 3 = 6$. Since $y = 6$ and not 0, the first equation is incorrect.

Test the second equation $y = 7x - 3$ with the first point (3, 0)

Substitute $x = 3$ into the equation: $y = 7(3) - 3 = 21 - 3 = 18$. Since $y = 18$ and not 0, the second equation is incorrect.

Test the third equation $y = x - 3$ with the first point (3, 0)

Substitute $x = 3$ into the equation: $y = 3 - 3 = 0$. The equation holds true for the first point. Now, let's test it with other points.

Test the third equation $y = x - 3$ with the second point (4, 1)

Substitute $x = 4$ into the equation: $y = 4 - 3 = 1$. The equation holds true for the second point.

Test the third equation $y = x - 3$ with the third point (5, 2)

Substitute $x = 5$ into the equation: $y = 5 - 3 = 2$. The equation holds true for the third point.

Test the third equation $y = x - 3$ with the fourth point (6, 3)

Substitute $x = 6$ into the equation: $y = 6 - 3 = 3$. The equation holds true for the fourth point.

Test the fourth equation $y = 5x - 3$ with the first point (3, 0)

Substitute $x = 3$ into the equation: $y = 5(3) - 3 = 15 - 3 = 12$. Since $y = 12$ and not 0, the fourth equation is incorrect.

Conclusion

Since the equation $y = x - 3$ holds true for all the points in the table, it is the correct equation.

$y = x - 3$

More Information

The equation $y = x - 3$ represents a linear relationship where the y-value is always 3 less than the x-value.

Tips

A common mistake is to only check the equation with one or two points. To ensure the equation is correct, it must be verified with all points in the table.