To answer your questions, let's analyze the provided graph.
a. The constant of proportionality is: Let's assume the graph represents water use (y-axis) against a certain variable (x-axis) like time or quantity of something related to water use. To find the constant of proportionality, we would typically find the ratio of water use to the other variable. However, since we don't have specific data points or labels, we can infer it from the increments. If, for example, water use increases by 10 for every increase of 1 on the x-axis, then the constant of proportionality would be 10.
b. Write an equation that represents the linear graph: A linear equation generally takes the form \( y = mx + b \). If we assume that the constant of proportionality is 10 (as we estimated above) and there is no y-intercept (the line goes through the origin), then the equation representing the linear graph would be \( y = 10x \).
c. This is a proportional relationship because the graph shows: This is a proportional relationship because the graph shows a straight line that passes through the origin (0,0) with a constant rate of change. This indicates that as one variable increases, the other variable (water use) increases at a consistent ratio.
If you provide specific points from the graph, I can refine these answers further!
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