Question

which ordered pairs represent points on the graph of this equation? select all that app
$2x = -\frac{1}{2}y$
(0, 0) (-6, -1)
(4, 6) (0, -4)
(4, -2) (-1, 4)

Explanation:

Step1: Recall the equation

The given equation is \(2x = -\frac{1}{2}y\), we can simplify it to \(y=-4x\) (multiply both sides by -2).

Step2: Check each ordered pair

• For \((0,0)\): Substitute \(x = 0\) into \(y=-4x\), we get \(y = 0\). So \((0,0)\) is on the graph.
• For \((-6,-1)\): Substitute \(x=-6\) into \(y=-4x\), we get \(y=-4\times(-6)=24

eq - 1\). So \((-6,-1)\) is not on the graph.

• For \((4,6)\): Substitute \(x = 4\) into \(y=-4x\), we get \(y=-4\times4=-16

eq6\). So \((4,6)\) is not on the graph.

• For \((0,-4)\): Substitute \(x = 0\) into \(y=-4x\), we get \(y = 0

eq - 4\). So \((0,-4)\) is not on the graph.

• For \((4,-2)\): Substitute \(x = 4\) into \(y=-4x\), we get \(y=-4\times4=-16

eq - 2\). Wait, no, wait, original equation: \(2x=-\frac{1}{2}y\), for \((4,-2)\): Left side \(2\times4 = 8\), Right side \(-\frac{1}{2}\times(-2)=1\), \(8
eq1\). Wait, earlier simplification: \(2x=-\frac{1}{2}y\) multiply both sides by 2: \(4x=-y\) or \(y = - 4x\). For \((-1,4)\): Substitute \(x=-1\) into \(y=-4x\), we get \(y=-4\times(-1)=4\). So \((-1,4)\) is on the graph. Wait, let's re - check \((4,-2)\) with original equation: \(2\times4=8\), \(-\frac{1}{2}\times(-2) = 1\), \(8
eq1\). \((-1,4)\): \(2\times(-1)=-2\), \(-\frac{1}{2}\times4=-2\). So \((-1,4)\) is on the graph. \((0,0)\): \(2\times0 = 0\), \(-\frac{1}{2}\times0 = 0\), so it's on the graph.

Wait, let's do it step by step for each:

1. \((0,0)\):

Left side of \(2x=-\frac{1}{2}y\): \(2\times0 = 0\)
Right side: \(-\frac{1}{2}\times0 = 0\)
So \(0 = 0\), valid.

1. \((-6,-1)\):

Left side: \(2\times(-6)=-12\)
Right side: \(-\frac{1}{2}\times(-1)=\frac{1}{2}\)
\(-12
eq\frac{1}{2}\), invalid.

1. \((4,6)\):

Left side: \(2\times4 = 8\)
Right side: \(-\frac{1}{2}\times6=-3\)
\(8
eq - 3\), invalid.

1. \((0,-4)\):

Left side: \(2\times0 = 0\)
Right side: \(-\frac{1}{2}\times(-4)=2\)
\(0
eq2\), invalid.

1. \((4,-2)\):

Left side: \(2\times4 = 8\)
Right side: \(-\frac{1}{2}\times(-2)=1\)
\(8
eq1\), invalid.

1. \((-1,4)\):

Left side: \(2\times(-1)=-2\)
Right side: \(-\frac{1}{2}\times4=-2\)
\(-2=-2\), valid.

Answer:

The ordered pairs that represent points on the graph are \((0,0)\) and \((-1,4)\)