The equation 3x-2y=4 is graphed in the xy-plane. Which of the statements is true of its graph? Choose 1 answer: (A) The graph is a line parallel to the line whose equation is y=-(2)/(3)x+1. B The graph is a line perpendicular to the line whose equation is y=-(2)/(3)x+1. (C) The graph is a line with a slope of -(2)/(3). (D) The graph is a line with a slope of -(3)/(2).

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Rephrase Prompt: First, let's rephrase the  ＂What is the characteristic of the graph of the equation 3x - 2y = 4 in relation to the line y = -(2/3)x + 1?＂Find Slope: To determine the characteristics of the graph of the equation 3x - 2y = 4, we need to find its slope. We can do this by rewriting the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.Convert to Slope-Intercept Form: Let's solve for y in the equation 3x - 2y = 4 to get it into slope-intercept form: 3x - 2y = 4 -2y = -3x + 4 y = (3/2)x - 2Determine Slope: Now that we have the equation in slope-intercept form, we can see that the slope (m) of the line is 3/2. This means that the graph of the equation is a line with a slope of 3/2.Compare Slopes: Let's compare the slope of our line with the slope of the line given in the answer choices. The line y = -(2/3)x + 1 has a slope of -2/3. Since the slopes are not the same and not opposite reciprocals, the lines are neither parallel nor perpendicular.Correct Answer: The correct statement about the graph of the equation 3x - 2y = 4 is that it is a line with a slope of 3/2. This means that option (D) is the correct answer, as it states the graph is a line with a slope of -(3/2), which is the negative reciprocal of the slope of the line given in the question prompt.

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