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Which of the following statements is true about the graph shown?

a.The equation y = 4.5x is correctly represented by the graph.
b.The graph is incorrect and the line should go through the point (3, 13.5).
c.The graph is incorrect and the line should go through the point (4.5, 4.5).
d.The graph does not show a proportional relationship.

User AngelGris
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1 Answer

4 votes

Final answer:

The correct statement is option (b) as the graph of the given equation y = 4.5x should indeed pass through the point (3, 13.5) to accurately represent the equation.

Step-by-step explanation:

To determine which statement about the graph of a line is true, we need to understand the properties of linear equations and graphing lines. If we are given the equation y = 4.5x, it means that the slope (rate of change of y with respect to x) is 4.5. Therefore, for every one unit that x increases, y increases by 4.5 units.

The graph of this equation would be a straight line passing through the origin (0,0) because the y-intercept is zero.

Given that option (b) mentions the graph should go through the point (3, 13.5), we can test it by plugging x = 3 into the equation to see if y equals 13.5: y = 4.5 * 3 = 13.5, which confirms the point (3, 13.5) is on the line represented by y = 4.5x.

Hence, if the graph does not pass through (3, 13.5), it is not correctly representing the equation y = 4.5x. As for option (c), a point (4.5, 4.5) would not be on the line since y = 4.5 * 4.5 is actually 20.25.

Lastly, since the equation y = 4.5x shows a direct variation with a constant rate (slope), the graph does show a proportional relationship between x and y, contradicting statement (d). Therefore, the correct answer is (b) The graph is incorrect and the line should go through the point (3, 13.5).

User Kgadek
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7.9k points