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Line A passes through the points (−2,27)(-2,27) and (1,−9)(1,-9). Line B passes through the points (−1,15)(-1,15) and (3,−33)(3,-33). Which statement is true?\newlineChoices:\newline(A) Line A does not intersect line B.\newline(B) Line A overlaps line B.\newline(C) Line A intersects line B at exactly one point.

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Q. Line A passes through the points (−2,27)(-2,27) and (1,−9)(1,-9). Line B passes through the points (−1,15)(-1,15) and (3,−33)(3,-33). Which statement is true?\newlineChoices:\newline(A) Line A does not intersect line B.\newline(B) Line A overlaps line B.\newline(C) Line A intersects line B at exactly one point.
  1. Calculate Slope Line A: Calculate the slope of Line A using the points (−2,27)(-2,27) and (1,−9)(1,-9).\newlineSlope formula: m=(y2−y1)(x2−x1)m = \frac{(y_2 - y_1)}{(x_2 - x_1)}\newlinem=(−9−27)(1−(−2))m = \frac{(-9 - 27)}{(1 - (-2))}\newlinem=(−36)3m = \frac{(-36)}{3}\newlinem=−12m = -12
  2. Calculate Slope Line B: Calculate the slope of Line B using the points (−1,15)(-1,15) and (3,−33)(3,-33).\newlineSlope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}\newlinem=−33−153−(−1)m = \frac{-33 - 15}{3 - (-1)}\newlinem=−484m = \frac{-48}{4}\newlinem=−12m = -12
  3. Compare Slopes: Compare the slopes of Line A and Line B.\newlineBoth Line A and Line B have the same slope, m=−12m = -12.\newlineSince the slopes are equal, the lines are either parallel or overlapping.
  4. Check Y-Intercepts: Check if Line A and Line B are the same line by finding the y-intercept of each line.\newlineFor Line A, using point (−2,27)(-2,27) and slope −12-12:\newliney−y1=m(x−x1)y - y_1 = m(x - x_1)\newline27−(−12)(−2−x)27 - (-12)(-2 - x)\newline27=−12x−2427 = -12x - 24\newline51=−12x51 = -12x\newlinex=−5112x = -\frac{51}{12}\newlineThis calculation is incorrect; we should be finding y-intercept bb, not xx.

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