QUESTION IMAGE
Question
which ordered pairs represent points on the graph of this equation? select all that apply.
$6y = 7x - 4$
$(-4, 3)$ $(6, -7)$ $(2, -4)$
$(4, 4)$ $(-6, 3)$ $(-2, -3)$
To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(6y = 7x - 4\), we substitute the \(x\) and \(y\) values of each ordered pair into the equation and check if both sides are equal.
For \((-4, 3)\):
Substitute \(x = -4\), \(y = 3\):
Left - hand side (LHS): \(6y=6\times3 = 18\)
Right - hand side (RHS): \(7x - 4=7\times(-4)-4=-28 - 4=-32\)
Since \(18
eq - 32\), \((-4, 3)\) is not on the graph.
For \((6, -7)\):
Substitute \(x = 6\), \(y=-7\):
LHS: \(6y = 6\times(-7)=-42\)
RHS: \(7x - 4=7\times6-4 = 42 - 4 = 38\)
Since \(-42
eq38\), \((6, -7)\) is not on the graph.
For \((2, -4)\):
Substitute \(x = 2\), \(y = -4\):
LHS: \(6y=6\times(-4)=-24\)
RHS: \(7x - 4=7\times2-4=14 - 4 = 10\)
Since \(-24
eq10\), \((2, -4)\) is not on the graph.
For \((4, 4)\):
Substitute \(x = 4\), \(y = 4\):
LHS: \(6y=6\times4 = 24\)
RHS: \(7x - 4=7\times4-4=28 - 4 = 24\)
Since \(24 = 24\), \((4, 4)\) is on the graph.
For \((-6, 3)\):
Substitute \(x=-6\), \(y = 3\):
LHS: \(6y=6\times3=18\)
RHS: \(7x - 4=7\times(-6)-4=-42 - 4=-46\)
Since \(18
eq - 46\), \((-6, 3)\) is not on the graph.
For \((-2, -3)\):
Substitute \(x=-2\), \(y=-3\):
LHS: \(6y=6\times(-3)=-18\)
RHS: \(7x - 4=7\times(-2)-4=-14 - 4=-18\)
Since \(-18=-18\), \((-2, -3)\) is on the graph.
So the ordered pairs that lie on the graph of \(6y = 7x - 4\) are \(\boldsymbol{(4, 4)}\) and \(\boldsymbol{(-2, -3)}\).
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To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(6y = 7x - 4\), we substitute the \(x\) and \(y\) values of each ordered pair into the equation and check if both sides are equal.
For \((-4, 3)\):
Substitute \(x = -4\), \(y = 3\):
Left - hand side (LHS): \(6y=6\times3 = 18\)
Right - hand side (RHS): \(7x - 4=7\times(-4)-4=-28 - 4=-32\)
Since \(18
eq - 32\), \((-4, 3)\) is not on the graph.
For \((6, -7)\):
Substitute \(x = 6\), \(y=-7\):
LHS: \(6y = 6\times(-7)=-42\)
RHS: \(7x - 4=7\times6-4 = 42 - 4 = 38\)
Since \(-42
eq38\), \((6, -7)\) is not on the graph.
For \((2, -4)\):
Substitute \(x = 2\), \(y = -4\):
LHS: \(6y=6\times(-4)=-24\)
RHS: \(7x - 4=7\times2-4=14 - 4 = 10\)
Since \(-24
eq10\), \((2, -4)\) is not on the graph.
For \((4, 4)\):
Substitute \(x = 4\), \(y = 4\):
LHS: \(6y=6\times4 = 24\)
RHS: \(7x - 4=7\times4-4=28 - 4 = 24\)
Since \(24 = 24\), \((4, 4)\) is on the graph.
For \((-6, 3)\):
Substitute \(x=-6\), \(y = 3\):
LHS: \(6y=6\times3=18\)
RHS: \(7x - 4=7\times(-6)-4=-42 - 4=-46\)
Since \(18
eq - 46\), \((-6, 3)\) is not on the graph.
For \((-2, -3)\):
Substitute \(x=-2\), \(y=-3\):
LHS: \(6y=6\times(-3)=-18\)
RHS: \(7x - 4=7\times(-2)-4=-14 - 4=-18\)
Since \(-18=-18\), \((-2, -3)\) is on the graph.
So the ordered pairs that lie on the graph of \(6y = 7x - 4\) are \(\boldsymbol{(4, 4)}\) and \(\boldsymbol{(-2, -3)}\).