If a graph is proportional, what characteristics does it display?
A. It will have y-values larger than their corresponding x-values
B. It will curve
C.It will climb rapidly, indicating a steep slope
D. It will pass through the point (0,0)
D. It will pass through the point (0,0).
D. It will pass through the point (0,0)
To determine the characteristics of a proportional graph, you need to understand what it means for a graph to be proportional. A graph is considered proportional if it represents a direct variation relationship between two variables. In other words, as one variable increases, the other variable also increases or decreases by a constant ratio.
From the options provided, the characteristic that a proportional graph will definitely display is option D. It will pass through the point (0,0). This is because for a graph to be proportional, when both variables are zero, the output or dependent variable (y-value) must also be zero.
The other options are not necessarily true for all proportional graphs. Let's analyze them:
A. It will have y-values larger than their corresponding x-values: This is not always true for a proportional graph. Depending on the context of the problem, the values of x and y could be both positive, resulting in comparable values.
B. It will curve: Proportional graphs do not typically curve. They usually represent a straight line or are linear in nature. Curved graphs would indicate a nonlinear relationship between the two variables.
C. It will climb rapidly, indicating a steep slope: While a steep slope can indicate a proportional relationship, it is not a characteristic that all proportional graphs will display. The steepness of the slope depends on the specific values of the constant ratio.
Therefore, out of the given options, the correct characteristic of a proportional graph is D. It will pass through the point (0,0).