Which equation is represented by the function?

Understand the Problem

The question is asking to identify which equation corresponds to a given set of x and y values from a table. We need to analyze the data to find the correct equation among the provided options.

Answer

The equation is $ y = -x - 3 $.

Steps to Solve

Identify the points from the table

Extract the points given in the table for $(x, y)$:

$(-4, 1)$
$(1, -4)$
$(6, -9)$
$(11, -14)$

Substitute the points into the equations

You can test each equation option by substituting the $x$ values to see if they yield the corresponding $y$ values.

For $y = -x + 3$:
- When $x = -4$: $y = -(-4) + 3 = 4 + 3 = 7$ (not a match)
- When $x = 1$: $y = -1 + 3 = 2$ (not a match)
For $y = x - 3$:
- When $x = -4$: $y = -4 - 3 = -7$ (not a match)
- When $x = 1$: $y = 1 - 3 = -2$ (not a match)
For $y = x + 3$:
- When $x = -4$: $y = -4 + 3 = -1$ (not a match)
- When $x = 1$: $y = 1 + 3 = 4$ (not a match)
For $y = -x - 3$:
- When $x = -4$: $y = -(-4) - 3 = 4 - 3 = 1$ (match)
- When $x = 1$: $y = -1 - 3 = -4$ (match)
- When $x = 6$: $y = -6 - 3 = -9$ (match)
- When $x = 11$: $y = -11 - 3 = -14$ (match)

Confirm the correct equation

Since all the table points match the equation $y = -x - 3$, this is the correct equation.

The correct equation is ( y = -x - 3 ).

More Information

This equation represents a linear function with a negative slope. It shows that as ( x ) increases, ( y ) decreases.

Tips

Failing to check all points against the equations can lead to an incorrect conclusion.
Miscalculating the ( y ) values during substitution can also result in errors.

AI-generated content may contain errors. Please verify critical information

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