Question

which ordered pairs represent points on the graph of this equation? select all that apply.

$y = -3x$

$(-1, 3)$ $(-6, -4)$ $(3, 1)$

$(6, 4)$ $(-2, 6)$ $(2, -6)$

Explanation:

To determine which ordered pairs \((x, y)\) lie on the graph of \(y = -3x\), we substitute the \(x\)-value of each ordered pair into the equation and check if the resulting \(y\)-value matches the one in the pair.

Step 1: Check \((-1, 3)\)

Substitute \(x = -1\) into \(y = -3x\):
\(y = -3(-1) = 3\).
The \(y\)-value from the equation (\(3\)) matches the \(y\)-value in the ordered pair (\(3\)). So, \((-1, 3)\) is on the graph.

Step 2: Check \((-6, -4)\)

Substitute \(x = -6\) into \(y = -3x\):
\(y = -3(-6) = 18\).
The \(y\)-value from the equation (\(18\)) does not match the \(y\)-value in the ordered pair (\(-4\)). So, \((-6, -4)\) is not on the graph.

Step 3: Check \((3, 1)\)

Substitute \(x = 3\) into \(y = -3x\):
\(y = -3(3) = -9\).
The \(y\)-value from the equation (\(-9\)) does not match the \(y\)-value in the ordered pair (\(1\)). So, \((3, 1)\) is not on the graph.

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

Substitute \(x = 6\) into \(y = -3x\):
\(y = -3(6) = -18\).
The \(y\)-value from the equation (\(-18\)) does not match the \(y\)-value in the ordered pair (\(4\)). So, \((6, 4)\) is not on the graph.

Step 5: Check \((-2, 6)\)

Substitute \(x = -2\) into \(y = -3x\):
\(y = -3(-2) = 6\).
The \(y\)-value from the equation (\(6\)) matches the \(y\)-value in the ordered pair (\(6\)). So, \((-2, 6)\) is on the graph.

Step 6: Check \((2, -6)\)

Substitute \(x = 2\) into \(y = -3x\):
\(y = -3(2) = -6\).
The \(y\)-value from the equation (\(-6\)) matches the \(y\)-value in the ordered pair (\(-6\)). So, \((2, -6)\) is on the graph.

Answer:

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