Question

which ordered pairs represent points on the graph of this equation? select all that apply.
3x = y + 4
(0, 4) (-1, -7) (0, -4)
(2, 2) (3, 5) (7, -1)

Explanation:

To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(3x = y + 4\), we substitute the \(x\)- and \(y\)-values of each ordered pair into the equation and check if the equation holds true.

Step 1: Check \((0, 4)\)

Substitute \(x = 0\) and \(y = 4\) into \(3x = y + 4\):
Left-hand side (LHS): \(3(0) = 0\)
Right-hand side (RHS): \(4 + 4 = 8\)
Since \(0
eq 8\), \((0, 4)\) is not on the graph.

Step 2: Check \((-1, -7)\)

Substitute \(x = -1\) and \(y = -7\) into \(3x = y + 4\):
LHS: \(3(-1) = -3\)
RHS: \(-7 + 4 = -3\)
Since \(-3 = -3\), \((-1, -7)\) is on the graph.

Step 3: Check \((0, -4)\)

Substitute \(x = 0\) and \(y = -4\) into \(3x = y + 4\):
LHS: \(3(0) = 0\)
RHS: \(-4 + 4 = 0\)
Since \(0 = 0\), \((0, -4)\) is on the graph.

Step 4: Check \((2, 2)\)

Substitute \(x = 2\) and \(y = 2\) into \(3x = y + 4\):
LHS: \(3(2) = 6\)
RHS: \(2 + 4 = 6\)
Since \(6 = 6\), \((2, 2)\) is on the graph.

Step 5: Check \((3, 5)\)

Substitute \(x = 3\) and \(y = 5\) into \(3x = y + 4\):
LHS: \(3(3) = 9\)
RHS: \(5 + 4 = 9\)
Since \(9 = 9\), \((3, 5)\) is on the graph.

Step 6: Check \((7, -1)\)

Substitute \(x = 7\) and \(y = -1\) into \(3x = y + 4\):
LHS: \(3(7) = 21\)
RHS: \(-1 + 4 = 3\)
Since \(21
eq 3\), \((7, -1)\) is not on the graph.

Final Valid Ordered Pairs:

• \((-1, -7)\)
• \((0, -4)\)
• \((2, 2)\)
• \((3, 5)\)

The incorrect ordered pairs are \((0, 4)\) and \((7, -1)\). The correct ones are \(\boldsymbol{(-1, -7)}\), \(\boldsymbol{(0, -4)}\), \(\boldsymbol{(2, 2)}\), and \(\boldsymbol{(3, 5)}\).

Answer:

To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(3x = y + 4\), we substitute the \(x\)- and \(y\)-values of each ordered pair into the equation and check if the equation holds true.

Step 1: Check \((0, 4)\)

Substitute \(x = 0\) and \(y = 4\) into \(3x = y + 4\):
Left-hand side (LHS): \(3(0) = 0\)
Right-hand side (RHS): \(4 + 4 = 8\)
Since \(0
eq 8\), \((0, 4)\) is not on the graph.

Step 2: Check \((-1, -7)\)

Substitute \(x = -1\) and \(y = -7\) into \(3x = y + 4\):
LHS: \(3(-1) = -3\)
RHS: \(-7 + 4 = -3\)
Since \(-3 = -3\), \((-1, -7)\) is on the graph.

Step 3: Check \((0, -4)\)

Substitute \(x = 0\) and \(y = -4\) into \(3x = y + 4\):
LHS: \(3(0) = 0\)
RHS: \(-4 + 4 = 0\)
Since \(0 = 0\), \((0, -4)\) is on the graph.

Step 4: Check \((2, 2)\)

Substitute \(x = 2\) and \(y = 2\) into \(3x = y + 4\):
LHS: \(3(2) = 6\)
RHS: \(2 + 4 = 6\)
Since \(6 = 6\), \((2, 2)\) is on the graph.

Step 5: Check \((3, 5)\)

Substitute \(x = 3\) and \(y = 5\) into \(3x = y + 4\):
LHS: \(3(3) = 9\)
RHS: \(5 + 4 = 9\)
Since \(9 = 9\), \((3, 5)\) is on the graph.

Step 6: Check \((7, -1)\)

Substitute \(x = 7\) and \(y = -1\) into \(3x = y + 4\):
LHS: \(3(7) = 21\)
RHS: \(-1 + 4 = 3\)
Since \(21
eq 3\), \((7, -1)\) is not on the graph.

Final Valid Ordered Pairs:

• \((-1, -7)\)
• \((0, -4)\)
• \((2, 2)\)
• \((3, 5)\)

The incorrect ordered pairs are \((0, 4)\) and \((7, -1)\). The correct ones are \(\boldsymbol{(-1, -7)}\), \(\boldsymbol{(0, -4)}\), \(\boldsymbol{(2, 2)}\), and \(\boldsymbol{(3, 5)}\).