Question

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

Explanation:

To determine which ordered pairs \((x, y)\) satisfy the equation \(5x = -4y\), we substitute the \(x\) and \(y\) values of each ordered pair into the equation and check if both sides are equal.

Step 1: Check \((-4, 5)\)

Substitute \(x = -4\) and \(y = 5\) into the equation:
Left - hand side (LHS): \(5x=5\times(-4)=-20\)
Right - hand side (RHS): \(-4y=-4\times5 = - 20\)
Since \(LHS = RHS\), \((-4,5)\) is on the graph.

Step 2: Check \((0, 0)\)

Substitute \(x = 0\) and \(y = 0\) into the equation:
LHS: \(5x = 5\times0=0\)
RHS: \(-4y=-4\times0 = 0\)
Since \(LHS = RHS\), \((0,0)\) is on the graph.

Step 3: Check \((-4,-5)\)

Substitute \(x=-4\) and \(y = - 5\) into the equation:
LHS: \(5x=5\times(-4)=-20\)
RHS: \(-4y=-4\times(-5)=20\)
Since \(LHS=-20\) and \(RHS = 20\), \(LHS
eq RHS\), so \((-4,-5)\) is not on the graph.

Step 4: Check \((5,1)\)

Substitute \(x = 5\) and \(y = 1\) into the equation:
LHS: \(5x=5\times5 = 25\)
RHS: \(-4y=-4\times1=-4\)
Since \(25
eq - 4\), \((5,1)\) is not on the graph.

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

Substitute \(x = 4\) and \(y=-5\) into the equation:
LHS: \(5x=5\times4 = 20\)
RHS: \(-4y=-4\times(-5)=20\)
Since \(LHS = RHS\), \((4,-5)\) is on the graph.

Step 6: Check \((1,4)\)

Substitute \(x = 1\) and \(y = 4\) into the equation:
LHS: \(5x=5\times1=5\)
RHS: \(-4y=-4\times4=-16\)
Since \(5
eq - 16\), \((1,4)\) is not on the graph.

Answer:

The ordered pairs that represent points on the graph of \(5x=-4y\) are \((-4, 5)\), \((0, 0)\), and \((4, - 5)\)

So the correct ordered pairs are:
A. \((-4, 5)\)
B. \((0, 0)\)
F. \((4, - 5)\)