Question

which ordered pairs represent points on the graph of this equation? select all that apply. -3x + y = 3 (1, 6) (-1, 0) (5, -2) (-2, -3) (0, 3) (-3, -6)

Explanation:

Step1: Recall the equation

The given equation is \(-3x + y = 3\), which can be rewritten as \(y = 3x + 3\). We will substitute the \(x\)-value of each ordered pair into this equation and check if the resulting \(y\)-value matches the one in the pair.

Step2: Check \((1, 6)\)

Substitute \(x = 1\) into \(y = 3x + 3\):
\(y = 3(1) + 3 = 6\).
The \(y\)-value matches, so \((1, 6)\) is on the graph.

Step3: Check \((-1, 0)\)

Substitute \(x = -1\) into \(y = 3x + 3\):
\(y = 3(-1) + 3 = 0\).
The \(y\)-value matches, so \((-1, 0)\) is on the graph.

Step4: Check \((5, -2)\)

Substitute \(x = 5\) into \(y = 3x + 3\):
\(y = 3(5) + 3 = 18\).
\(18
eq -2\), so \((5, -2)\) is not on the graph.

Step5: Check \((-2, -3)\)

Substitute \(x = -2\) into \(y = 3x + 3\):
\(y = 3(-2) + 3 = -3\).
The \(y\)-value matches, so \((-2, -3)\) is on the graph.

Step6: Check \((0, 3)\)

Substitute \(x = 0\) into \(y = 3x + 3\):
\(y = 3(0) + 3 = 3\).
The \(y\)-value matches, so \((0, 3)\) is on the graph.

Step7: Check \((-3, -6)\)

Substitute \(x = -3\) into \(y = 3x + 3\):
\(y = 3(-3) + 3 = -6\).
The \(y\)-value matches, so \((-3, -6)\) is on the graph.

Answer:

The ordered pairs that represent points on the graph of \(-3x + y = 3\) are:
\((1, 6)\), \((-1, 0)\), \((-2, -3)\), \((0, 3)\), \((-3, -6)\)