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The equations 2y=-4x+8 and 2y=-4x+16 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 graphs of the two equations are parallel lines. (B) The graphs of the two equations are perpendicular lines. (c) The graphs have the same y-intercept. (D) The y-intercepts of the two graphs are reflected in the x-axis.

The equations 2y=−4x+8 2 y=-4 x+8 and 2y=−4x+16 2 y=-4 x+16 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 graphs of the two equations are parallel lines.\newline(B) The graphs of the two equations are perpendicular lines.\newline(C) The graphs have the same y y -intercept.\newline(D) The y y -intercepts of the two graphs are reflected in the x x -axis.

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Q. The equations 2y=−4x+8 2 y=-4 x+8 and 2y=−4x+16 2 y=-4 x+16 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 graphs of the two equations are parallel lines.\newline(B) The graphs of the two equations are perpendicular lines.\newline(C) The graphs have the same y y -intercept.\newline(D) The y y -intercepts of the two graphs are reflected in the x x -axis.
  1. Equation Analysis: Let's analyze the first equation 2y=−4x+82y = -4x + 8. To find the slope and y-intercept, we can put it in slope-intercept form, which is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Divide both sides by 22 to isolate yy. y=−2x+4y = -2x + 4 Here, the slope (mm) is −2-2 and the y-intercept (bb) is y=mx+by = mx + b00.
  2. Slope and Y-Intercept: Now let's analyze the second equation 2y=−4x+162y = -4x + 16. Again, we put it in slope-intercept form by dividing both sides by 22. y=−2x+8y = -2x + 8 Here, the slope (m)(m) is −2-2 and the y-intercept (b)(b) is 88.
  3. Comparison of Equations: Comparing the two equations, we see that they both have the same slope, −2-2, but different yy-intercepts, 44 and 88 respectively.\newlineSince they have the same slope, the lines are parallel to each other.
  4. Answer Choices: Now let's check the answer choices against our findings:\newline(A) The graphs of the two equations are parallel lines. This is true based on our analysis.\newline(B) The graphs of the two equations are perpendicular lines. This is false because perpendicular lines would have slopes that are negative reciprocals of each other.\newline(C) The graphs have the same yy-intercept. This is false because the yy-intercepts are 44 and 88.\newline(D) The yy-intercepts of the two graphs are reflected in the xx-axis. This is false because a reflection across the xx-axis would not change the xx-coordinate of the yy-intercept, but would change the sign of the yy-coordinate.

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