Final answer:
In comparing the provided equations, option c, y=x² +6, does not belong with the others because it is a quadratic equation, whereas options a, b, and d are linear equations.
Step-by-step explanation:
When determining which equation does not belong with the others, we need to analyze the form of each equation. Equations a, b, and d are in the form y = mx + b, where m is the slope and b is the y-intercept. This form describes a linear equation, represented graphically by a straight line.
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- a. y=0.5x-0.2
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- b. 4x+3=y
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- d. 3/4x+1/3=y
These three equations define lines with different slopes and y-intercepts, but they are linear nonetheless. On the other hand:
This equation is a quadratic equation because it includes an x squared term (x²). Graphically, a quadratic equation is represented by a parabola, which is a curve, not a straight line.
Therefore, the equation that does not belong with the other three is option c, y=x² +6, because it represents a quadratic function while the rest are linear equations.