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Line AA passes through the points (0,1)(0,1) and (8,−2)(8,-2). Line BB passes through the points (−8,2)(-8,2) and (16,−7)(16,-7). \newlineWhich statement is true?\newlineChoices:\newline(A) Line AA overlaps line BB.\newline(B) Line AA intersects line BB at exactly one point.\newline(C) Line AA does not intersect line BB.

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Slopes of parallel and perpendicular linesright chevron icon

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Q. Line AA passes through the points (0,1)(0,1) and (8,−2)(8,-2). Line BB passes through the points (−8,2)(-8,2) and (16,−7)(16,-7). \newlineWhich statement is true?\newlineChoices:\newline(A) Line AA overlaps line BB.\newline(B) Line AA intersects line BB at exactly one point.\newline(C) Line AA does not intersect line BB.
  1. Calculate slope Line A: Calculate the slope of Line A using the points (0,1)(0,1) and (8,−2)(8,-2).\newlineSlope formula: (y2−y1)(x2−x1)\frac{(y_2 - y_1)}{(x_2 - x_1)}\newlineSlope of Line A = (−2−1)(8−0)=−38\frac{(-2 - 1)}{(8 - 0)} = \frac{-3}{8}
  2. Calculate slope Line B: Calculate the slope of Line B using the points (−8,2)(-8,2) and (16,−7)(16,-7).\newlineSlope formula: y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}\newlineSlope of Line B = −7−216+8=−924=−38\frac{-7 - 2}{16 + 8} = \frac{-9}{24} = \frac{-3}{8}
  3. Compare slopes: Compare the slopes of Line A and Line B.\newlineBoth lines have the same slope of −38-\frac{3}{8}.\newlineSince they have the same slope, they are either parallel or the same line (coincident).
  4. Check coincident lines: Check if the lines are coincident by plugging one point from Line A into the equation of Line B.\newlineEquation of Line B from point (−8,2)(-8,2): y−2=−38(x+8)y - 2 = -\frac{3}{8}(x + 8)\newlineSubstitute point (0,1)(0,1) from Line A into this equation:\newline1−2=−38(0+8)1 - 2 = -\frac{3}{8}(0 + 8)\newline−1=−3-1 = -3

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