Question

which ordered pairs are solutions to the equation? select all that apply.
(-7, 1) (0, -1) (0, 6)
(-5, 5) (7, 5) (5, -7)

Explanation:

To determine which ordered pairs are solutions to the linear equation represented by the graph, we check if each ordered pair \((x, y)\) lies on the line. A point lies on the line if, when we plot \((x, y)\), it is on the graphed line.

Step 1: Analyze \((-7, 1)\)

Check the graph: When \(x = -7\), the \(y\)-value on the line is \(1\). So \((-7, 1)\) is on the line.

Step 2: Analyze \((0, -1)\)

Check the graph: When \(x = 0\), the \(y\)-intercept is \(-1\) (the line crosses the \(y\)-axis at \((0, -1)\)). So \((0, -1)\) is on the line.

Step 3: Analyze \((0, 6)\)

Check the graph: The line crosses the \(y\)-axis at \((0, -1)\), not \((0, 6)\). So \((0, 6)\) is not on the line.

Step 4: Analyze \((-5, 5)\)

Check the graph: When \(x = -5\), the \(y\)-value on the line is \(5\). So \((-5, 5)\) is on the line.

Step 5: Analyze \((7, 5)\)

Check the graph: When \(x = 7\), the \(y\)-value on the line is not \(5\) (from the graph's trend, it should be negative). So \((7, 5)\) is not on the line.

Step 6: Analyze \((5, -7)\)

Check the graph: When \(x = 5\), the \(y\)-value on the line is \(-7\). So \((5, -7)\) is on the line.

Answer:

The correct ordered pairs (solutions) are:
\((-7, 1)\), \((0, -1)\), \((-5, 5)\), \((5, -7)\)

(Note: \((0, 6)\) and \((7, 5)\) are not on the line, so they are not solutions.)