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).