Question

which ordered pairs represent points on the graph of this equation? select all that apply.
$6y = 7x - 4$
$(6, -7)$ $(4, 4)$ $(-4, 3)$
$(2, -4)$ $(-2, -3)$ $(-6, 3)$
submit
work it out

Explanation:

To determine if an ordered pair \((x, y)\) is on the graph of the equation \(6y = 7x - 4\), we substitute the \(x\) and \(y\) values of the ordered pair into the equation and check if both sides are equal.

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

Substitute \(x = 6\) and \(y = -7\) into the equation:
Left side: \(6y = 6\times(-7) = -42\)
Right side: \(7x - 4 = 7\times6 - 4 = 42 - 4 = 38\)
Since \(-42
eq38\), \((6, -7)\) is not on the graph.

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

Substitute \(x = 4\) and \(y = 4\) into the equation:
Left side: \(6y = 6\times4 = 24\)
Right side: \(7x - 4 = 7\times4 - 4 = 28 - 4 = 24\)
Since \(24 = 24\), \((4, 4)\) is on the graph.

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

Substitute \(x = -4\) and \(y = 3\) into the equation:
Left side: \(6y = 6\times3 = 18\)
Right side: \(7x - 4 = 7\times(-4) - 4 = -28 - 4 = -32\)
Since \(18
eq -32\), \((-4, 3)\) is not on the graph.

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

Substitute \(x = 2\) and \(y = -4\) into the equation:
Left side: \(6y = 6\times(-4) = -24\)
Right side: \(7x - 4 = 7\times2 - 4 = 14 - 4 = 10\)
Since \(-24
eq10\), \((2, -4)\) is not on the graph.

Step 5: Check \((-2, -3)\)

Substitute \(x = -2\) and \(y = -3\) into the equation:
Left side: \(6y = 6\times(-3) = -18\)
Right side: \(7x - 4 = 7\times(-2) - 4 = -14 - 4 = -18\)
Since \(-18 = -18\), \((-2, -3)\) is on the graph.

Step 6: Check \((-6, 3)\)

Substitute \(x = -6\) and \(y = 3\) into the equation:
Left side: \(6y = 6\times3 = 18\)
Right side: \(7x - 4 = 7\times(-6) - 4 = -42 - 4 = -46\)
Since \(18
eq -46\), \((-6, 3)\) is not on the graph.

Answer:

The ordered pairs that represent points on the graph of the equation \(6y = 7x - 4\) are:

• \((4, 4)\)
• \((-2, -3)\)