What is the slope of the line shown on the graph

Rationale

The slope of the line shown on the graph is 13.

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. In this case, the line rises steeply, indicating a positive slope, which is calculated as the change in y divided by the change in x, resulting in a slope value of 13.

A (-0.333333333) YOUR ANSWER

This choice indicates a negative slope, suggesting that the line would be descending from left to right. However, the graph clearly shows an ascending line, which contradicts this option as it does not represent the correct relationship between the x and y coordinates.

B (-3) YOUR ANSWER

Similar to option A, a slope of -3 suggests a steep decline in the graph. Since the line is actually rising, this option is incorrect as it does not correspond to the observed increase in the y-values as the x-values increase.

C (3) YOUR ANSWER

While a slope of 3 indicates a positive relationship, it is not steep enough to match the observed angle of the line on the graph. The correct slope is significantly greater, as indicated by the line's steep ascent, making this option insufficient.

D (13) CORRECT

This choice accurately reflects the steep rise of the line on the graph, confirming that for every unit increase in the x-direction, the y-value increases by 13 units. This corresponds perfectly with the visual representation of the graph.

Conclusion

The slope of a line is a crucial aspect of understanding its behavior in a coordinate system. In this case, a slope of 13 accurately describes the steep upward trend observed in the graph. The other choices either suggest a downward trend or an insufficient increase, highlighting the importance of accurate slope calculation in graphical analysis.

What is the slope of the line shown on the graph

The slope of the line shown on the graph is 13.

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