What is the slope of the line represented by the table?
The slope of the line represented by the table is -2.
The slope is calculated by taking the change in the y-values divided by the change in the x-values between two points on the line. In this case, the slope of -2 indicates that for every unit increase in the x-direction, the y-value decreases by 2 units.
A slope of -4 suggests that for every increase of 1 in the x-direction, the y-value would decrease by 4. However, this does not match the rate of change observed in the table, where a decrease of 2 in y corresponds to an increase of 1 in x.
A slope of -2.5 would imply that for each unit increase in x, the y-value decreases by 2.5 units. This value is also inconsistent with the observed changes in y relative to x from the table, indicating that the slope is more accurately defined as -2.
A slope of -0.5 indicates a much gentler decline, meaning that for every unit increase in x, the y-value would only decrease by 0.5. This is clearly not representative of the steep decline reflected in the table, where the y-values drop more sharply.
The slope of a line is a crucial aspect of its representation, indicating the rate of change between two variables. In this instance, the accurate calculation reveals a slope of -2, confirming that for every increase of 1 in the x-values, the y-values drop by 2. The other choices do not align with the data presented in the table, reaffirming that -2 is the only correct interpretation of the slope in this context.
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