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The equations x+y=3 and -5x-5y=-15 are graphed in the xy-plane. Which of the following must be true of the graphs of the two equations? Choose 1 answer: A The slope of the graph of x+y=3 is 1 and the slope of the graph of -5x-5y=-15 is -1 . (B) The graphs of the two equations are perpendicular lines. (C) The y-intercept of the graph of -5x-5y=-15 is -15 . (D) The graphs of the two equations are the same line.

The equations x+y=3 x+y=3 and −5x−5y=−15 -5 x-5 y=-15 are graphed in the xy x y -plane. Which of the following must be true of the graphs of the two equations?\newlineChoose 11 answer:\newline(A) The slope of the graph of x+y=3 x+y=3 is 11 and the slope of the graph of −5x−5y=−15 -5 x-5 y=-15 is −1-1 .\newline(B) The graphs of the two equations are perpendicular lines.\newline(C) The y y -intercept of the graph of −5x−5y=−15 -5 x-5 y=-15 is −15-15 .\newline(D) The graphs of the two equations are the same line.

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Q. The equations x+y=3 x+y=3 and −5x−5y=−15 -5 x-5 y=-15 are graphed in the xy x y -plane. Which of the following must be true of the graphs of the two equations?\newlineChoose 11 answer:\newline(A) The slope of the graph of x+y=3 x+y=3 is 11 and the slope of the graph of −5x−5y=−15 -5 x-5 y=-15 is −1-1 .\newline(B) The graphs of the two equations are perpendicular lines.\newline(C) The y y -intercept of the graph of −5x−5y=−15 -5 x-5 y=-15 is −15-15 .\newline(D) The graphs of the two equations are the same line.
  1. Analyze first equation: Let's analyze the first equation x+y=3x + y = 3.\newlineTo find the slope, we can rewrite the equation in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.\newlinex+y=3x + y = 3 can be rewritten as y=−x+3y = -x + 3.\newlineHere, the slope (mm) is −1-1 and the y-intercept (bb) is 33.
  2. Analyze second equation: Now let's analyze the second equation -5x - 5y = -15＂).\(\newlineFirst, we simplify the equation by dividing all terms by \$-5\) to get \(x + y = 3\).\(\newline\)This is the same equation as the first one, which means the two lines are not distinct; they are the same line.\(\newline\)Therefore, they have the same slope, which is \(-1\), and the same y-intercept, which is \(3\).
  3. Evaluate answer choices: Now let's evaluate the answer choices given the information we have:\(\newline\)(A) The slope of the graph of \(x+y=3\) is \(1\) and the slope of the graph of \(-5x-5y=-15\) is \(-1\). This is incorrect because both slopes are \(-1\).\(\newline\)(B) The graphs of the two equations are perpendicular lines. This is incorrect because the lines are the same, not perpendicular.\(\newline\)(C) The y-intercept of the graph of \(-5x-5y=-15\) is \(-15\). This is incorrect because the y-intercept is \(3\), not \(-15\).\(\newline\)(D) The graphs of the two equations are the same line. This is correct because both equations simplify to the same line, \(x + y = 3\).

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