Based on the pairs of values in the table above, which of the following could express a relationship between x and y?
y=2x+2 expresses a relationship between x and y.
This equation correctly represents a linear relationship where the value of y is dependent on x, with a slope of 2 and a y-intercept of 2. The equation indicates that for every unit increase in x, y increases by 2 units, plus an additional 2 units from the intercept.
This equation suggests that for each unit increase in x, y increases by just 1 unit, plus 2. This does not match the given pairs in the table, where y increases at a rate that does not align with a slope of 1.
While this equation indicates a proportional relationship with a slope of 2, it lacks the constant term to account for the y-intercept. Thus, it does not correctly represent the relationship shown in the table, which requires an additional 2 units to accurately reflect the values of y.
This equation accurately captures the relationship demonstrated in the table, showing that y varies linearly with x at a rate of 2, starting from a y-intercept of 2. It effectively describes how y changes in relation to x based on the values provided.
This equation indicates a slope of 3, meaning that y would increase by 3 units for every unit increase in x, along with a constant 2. This does not align with the increments shown in the table, where the relationship between x and y is not consistent with a slope of 3.
The equation y=2x+2 best captures the linear relationship between x and y as described by the table values. It demonstrates the correct slope and intercept needed to accurately represent how y changes with x, while the other options fail to satisfy the conditions illustrated in the table. This understanding is crucial for analyzing linear relationships in algebra.
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