QUESTION IMAGE
Question
which ordered pairs represent points on the graph of this equation? select all that apply.
$2y = 4 - 5x$
$(0, -4)$ $(-7, 2)$ $(-2, 7)$
$(2, -3)$ $(0, 2)$ $(4, 3)$
To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(2y = 4 - 5x\), we substitute the \(x\)- and \(y\)-values of each ordered pair into the equation and check if the equation holds true.
For \((0, -4)\):
Substitute \(x = 0\) and \(y = -4\) into \(2y = 4 - 5x\):
Left-hand side (LHS): \(2(-4) = -8\)
Right-hand side (RHS): \(4 - 5(0) = 4\)
Since \(-8
eq 4\), \((0, -4)\) is not on the graph.
For \((-7, 2)\):
Substitute \(x = -7\) and \(y = 2\) into \(2y = 4 - 5x\):
LHS: \(2(2) = 4\)
RHS: \(4 - 5(-7) = 4 + 35 = 39\)
Since \(4
eq 39\), \((-7, 2)\) is not on the graph.
For \((-2, 7)\):
Substitute \(x = -2\) and \(y = 7\) into \(2y = 4 - 5x\):
LHS: \(2(7) = 14\)
RHS: \(4 - 5(-2) = 4 + 10 = 14\)
Since \(14 = 14\), \((-2, 7)\) is on the graph.
For \((2, -3)\):
Substitute \(x = 2\) and \(y = -3\) into \(2y = 4 - 5x\):
LHS: \(2(-3) = -6\)
RHS: \(4 - 5(2) = 4 - 10 = -6\)
Since \(-6 = -6\), \((2, -3)\) is on the graph.
For \((0, 2)\):
Substitute \(x = 0\) and \(y = 2\) into \(2y = 4 - 5x\):
LHS: \(2(2) = 4\)
RHS: \(4 - 5(0) = 4\)
Since \(4 = 4\), \((0, 2)\) is on the graph.
For \((4, 3)\):
Substitute \(x = 4\) and \(y = 3\) into \(2y = 4 - 5x\):
LHS: \(2(3) = 6\)
RHS: \(4 - 5(4) = 4 - 20 = -16\)
Since \(6
eq -16\), \((4, 3)\) is not on the graph.
Final Answer:
The ordered pairs on the graph are:
\(\boldsymbol{(-2, 7)}\), \(\boldsymbol{(2, -3)}\), \(\boldsymbol{(0, 2)}\)
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To determine which ordered pairs \((x, y)\) lie on the graph of the equation \(2y = 4 - 5x\), we substitute the \(x\)- and \(y\)-values of each ordered pair into the equation and check if the equation holds true.
For \((0, -4)\):
Substitute \(x = 0\) and \(y = -4\) into \(2y = 4 - 5x\):
Left-hand side (LHS): \(2(-4) = -8\)
Right-hand side (RHS): \(4 - 5(0) = 4\)
Since \(-8
eq 4\), \((0, -4)\) is not on the graph.
For \((-7, 2)\):
Substitute \(x = -7\) and \(y = 2\) into \(2y = 4 - 5x\):
LHS: \(2(2) = 4\)
RHS: \(4 - 5(-7) = 4 + 35 = 39\)
Since \(4
eq 39\), \((-7, 2)\) is not on the graph.
For \((-2, 7)\):
Substitute \(x = -2\) and \(y = 7\) into \(2y = 4 - 5x\):
LHS: \(2(7) = 14\)
RHS: \(4 - 5(-2) = 4 + 10 = 14\)
Since \(14 = 14\), \((-2, 7)\) is on the graph.
For \((2, -3)\):
Substitute \(x = 2\) and \(y = -3\) into \(2y = 4 - 5x\):
LHS: \(2(-3) = -6\)
RHS: \(4 - 5(2) = 4 - 10 = -6\)
Since \(-6 = -6\), \((2, -3)\) is on the graph.
For \((0, 2)\):
Substitute \(x = 0\) and \(y = 2\) into \(2y = 4 - 5x\):
LHS: \(2(2) = 4\)
RHS: \(4 - 5(0) = 4\)
Since \(4 = 4\), \((0, 2)\) is on the graph.
For \((4, 3)\):
Substitute \(x = 4\) and \(y = 3\) into \(2y = 4 - 5x\):
LHS: \(2(3) = 6\)
RHS: \(4 - 5(4) = 4 - 20 = -16\)
Since \(6
eq -16\), \((4, 3)\) is not on the graph.
Final Answer:
The ordered pairs on the graph are:
\(\boldsymbol{(-2, 7)}\), \(\boldsymbol{(2, -3)}\), \(\boldsymbol{(0, 2)}\)