In order to determine whether a slope is positive or negative based on a graph, we look at the direction of the line as we move from the left side of the graph to the right side.
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Positive Slope: A line has a positive slope if it rises as you move from left to right. This means that the y-values are increasing as the x-values increase. For example, if you imagine walking along the line from left to right, you would be going uphill.
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Negative Slope: A line has a negative slope if it falls as you move from left to right. This means that the y-values are decreasing as the x-values increase. In this case, if you were walking along the line from left to right, you would be going downhill.
Based on the responses you provided:
- “The slope is negative because the line decreases as you move from left to right on the graph.” (Correct) - This accurately describes a negative slope.
- “The slope is positive because the line increases as you move from left to right on the graph.” (Correct) - This accurately describes a positive slope.
- “The slope is negative because the line increases as you move from left to right on the graph.” (Incorrect) - A line that increases does not have a negative slope.
- “The slope is positive because the line decreases as you move from left to right on the graph.” (Incorrect) - A line that decreases does not have a positive slope.
In summary, the sign of the slope (positive or negative) is determined by the direction the line is moving as you go along the x-axis from left to right: rising gives positive and falling gives negative.