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 the equation holds true.
For \((-4, 3)\):
Substitute \(x = -4\) and \(y = 3\) into \(6y = 7x - 4\):
Left-hand side (LHS): \(6(3) = 18\)
Right-hand side (RHS): \(7(-4) - 4 = -28 - 4 = -32\)
Since \(18
eq -32\), \((-4, 3)\) is not on the graph.
For \((6, -7)\):
Substitute \(x = 6\) and \(y = -7\) into \(6y = 7x - 4\):
LHS: \(6(-7) = -42\)
RHS: \(7(6) - 4 = 42 - 4 = 38\)
Since \(-42
eq 38\), \((6, -7)\) is not on the graph.
For \((2, -4)\):
Substitute \(x = 2\) and \(y = -4\) into \(6y = 7x - 4\):
LHS: \(6(-4) = -24\)
RHS: \(7(2) - 4 = 14 - 4 = 10\)
Since \(-24
eq 10\), \((2, -4)\) is not on the graph.
For \((4, 4)\):
Substitute \(x = 4\) and \(y = 4\) into \(6y = 7x - 4\):
LHS: \(6(4) = 24\)
RHS: \(7(4) - 4 = 28 - 4 = 24\)
Since \(24 = 24\), \((4, 4)\) is on the graph.
For \((-6, 3)\):
Substitute \(x = -6\) and \(y = 3\) into \(6y = 7x - 4\):
LHS: \(6(3) = 18\)
RHS: \(7(-6) - 4 = -42 - 4 = -46\)
Since \(18
eq -46\), \((-6, 3)\) is not on the graph.
For \((-2, -3)\):
Substitute \(x = -2\) and \(y = -3\) into \(6y = 7x - 4\):
LHS: \(6(-3) = -18\)
RHS: \(7(-2) - 4 = -14 - 4 = -18\)
Since \(-18 = -18\), \((-2, -3)\) is on the graph.
Final Answer:
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 the equation holds true.
For \((-4, 3)\):
Substitute \(x = -4\) and \(y = 3\) into \(6y = 7x - 4\):
Left-hand side (LHS): \(6(3) = 18\)
Right-hand side (RHS): \(7(-4) - 4 = -28 - 4 = -32\)
Since \(18
eq -32\), \((-4, 3)\) is not on the graph.
For \((6, -7)\):
Substitute \(x = 6\) and \(y = -7\) into \(6y = 7x - 4\):
LHS: \(6(-7) = -42\)
RHS: \(7(6) - 4 = 42 - 4 = 38\)
Since \(-42
eq 38\), \((6, -7)\) is not on the graph.
For \((2, -4)\):
Substitute \(x = 2\) and \(y = -4\) into \(6y = 7x - 4\):
LHS: \(6(-4) = -24\)
RHS: \(7(2) - 4 = 14 - 4 = 10\)
Since \(-24
eq 10\), \((2, -4)\) is not on the graph.
For \((4, 4)\):
Substitute \(x = 4\) and \(y = 4\) into \(6y = 7x - 4\):
LHS: \(6(4) = 24\)
RHS: \(7(4) - 4 = 28 - 4 = 24\)
Since \(24 = 24\), \((4, 4)\) is on the graph.
For \((-6, 3)\):
Substitute \(x = -6\) and \(y = 3\) into \(6y = 7x - 4\):
LHS: \(6(3) = 18\)
RHS: \(7(-6) - 4 = -42 - 4 = -46\)
Since \(18
eq -46\), \((-6, 3)\) is not on the graph.
For \((-2, -3)\):
Substitute \(x = -2\) and \(y = -3\) into \(6y = 7x - 4\):
LHS: \(6(-3) = -18\)
RHS: \(7(-2) - 4 = -14 - 4 = -18\)
Since \(-18 = -18\), \((-2, -3)\) is on the graph.
Final Answer:
The ordered pairs that lie on the graph of \(6y = 7x - 4\) are:
\(\boldsymbol{(4, 4)}\) and \(\boldsymbol{(-2, -3)}\)