Question

which ordered pairs represent points on the graph of this equation? select all that apply.
2x - 5y = 11
(5, 7) (-8, 3) (3, -1)
(-2, -3) (8, 1) (-7, -5)

Explanation:

To determine if an ordered pair \((x, y)\) is on the graph of the equation \(2x - 5y = 11\), we substitute the \(x\) and \(y\) values of the ordered pair into the equation and check if the equation holds true.

Step 1: Check \((5, 7)\)

Substitute \(x = 5\) and \(y = 7\) into \(2x - 5y\):
\[
2(5) - 5(7) = 10 - 35 = -25
\]
Since \(-25
eq 11\), \((5, 7)\) is not on the graph.

Step 2: Check \((-8, 3)\)

Substitute \(x = -8\) and \(y = 3\) into \(2x - 5y\):
\[
2(-8) - 5(3) = -16 - 15 = -31
\]
Since \(-31
eq 11\), \((-8, 3)\) is not on the graph.

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

Substitute \(x = 3\) and \(y = -1\) into \(2x - 5y\):
\[
2(3) - 5(-1) = 6 + 5 = 11
\]
Since \(11 = 11\), \((3, -1)\) is on the graph.

Step 4: Check \((-2, -3)\)

Substitute \(x = -2\) and \(y = -3\) into \(2x - 5y\):
\[
2(-2) - 5(-3) = -4 + 15 = 11
\]
Since \(11 = 11\), \((-2, -3)\) is on the graph.

Step 5: Check \((8, 1)\)

Substitute \(x = 8\) and \(y = 1\) into \(2x - 5y\):
\[
2(8) - 5(1) = 16 - 5 = 11
\]
Since \(11 = 11\), \((8, 1)\) is on the graph.

Step 6: Check \((-7, -5)\)

Substitute \(x = -7\) and \(y = -5\) into \(2x - 5y\):
\[
2(-7) - 5(-5) = -14 + 25 = 11
\]
Since \(11 = 11\), \((-7, -5)\) is on the graph.

Answer:

The ordered pairs that represent points on the graph of \(2x - 5y = 11\) are:
\((3, -1)\), \((-2, -3)\), \((8, 1)\), \((-7, -5)\)