Question

which ordered pairs represent points on the graph of this equation? select all that apply.
7y = -4x + 28
(-6, 3) (-4, -5) (3, -6)
(0, 4) (5, 0) (-5, 1)

Explanation:

To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(7y = -4x + 28\), we substitute the \(x\)- and \(y\)-values of each ordered pair into the equation and check if both sides are equal.

For \((-6, 3)\):

Substitute \(x = -6\) and \(y = 3\) into \(7y = -4x + 28\):
Left - hand side (LHS): \(7(3)=21\)
Right - hand side (RHS): \(-4(-6)+28 = 24 + 28=52\)
Since \(21
eq52\), \((-6, 3)\) is not on the graph.

For \((-4, -5)\):

Substitute \(x=-4\) and \(y = -5\) into \(7y=-4x + 28\):
LHS: \(7(-5)=-35\)
RHS: \(-4(-4)+28=16 + 28 = 44\)
Since \(-35
eq44\), \((-4, -5)\) is not on the graph.

For \((3, -6)\):

Substitute \(x = 3\) and \(y=-6\) into \(7y=-4x + 28\):
LHS: \(7(-6)=-42\)
RHS: \(-4(3)+28=-12 + 28 = 16\)
Since \(-42
eq16\), \((3, -6)\) is not on the graph.

For \((0, 4)\):

Substitute \(x = 0\) and \(y = 4\) into \(7y=-4x + 28\):
LHS: \(7(4)=28\)
RHS: \(-4(0)+28=0 + 28 = 28\)
Since \(28 = 28\), \((0, 4)\) is on the graph.

For \((5, 0)\):

Substitute \(x = 5\) and \(y = 0\) into \(7y=-4x + 28\):
LHS: \(7(0)=0\)
RHS: \(-4(5)+28=-20 + 28 = 8\)
Since \(0
eq8\), \((5, 0)\) is not on the graph.

For \((-5, 1)\):

Substitute \(x=-5\) and \(y = 1\) into \(7y=-4x + 28\):
LHS: \(7(1)=7\)
RHS: \(-4(-5)+28=20 + 28 = 48\)
Since \(7
eq48\), \((-5, 1)\) is not on the graph.

Answer:

Only the ordered pair \(\boldsymbol{(0, 4)}\) lies on the graph of \(7y=-4x + 28\).