The correct response is:
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis negative 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is 23, so the system is inconsistent.
Determine if the system is inconsistent by graphing and finding the slopes.
y=23x+5
−4x+6y=12 (1 point)
Responses
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis negative 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is 32, so the system is inconsistent.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis negative 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is Start Fraction 3 over 2 End Fraction , so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is −32, so the system is inconsistent.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is negative Start Fraction 3 over 2 End Fraction , so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is −23, so the system is inconsistent.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two downward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is negative Start Fraction 2 over 3 End Fraction , so the system is inconsistent.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis negative 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis.
The slope of both lines is 23, so the system is inconsistent.
Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two upward slanting lines are plotted on the plane. A solid line with arrows at both ends passes through left parenthesis negative 8 comma 0 right parenthesis and left parenthesis 0 comma 5 right parenthesis. A dotted line with arrows at both ends passes through left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 2 right parenthesis. The slope of both lines is Start Fraction 2 over 3 End Fraction , so the system is inconsistent.
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