Line A passes through the points (4,9) and (12,23). Line B passes through the points (0,2) and (-8,-12). Which statement is true? Choices: (A)Line A intersects line B at exactly one point. (B)Line A does not intersect line B. (C)Line A overlaps line B.

Question

Line A passes through the points (4,9) and (12,23). Line B passes through the points (0,2) and (-8,-12). Which statement is true?    Choices: (A)Line A intersects line B at exactly one point. (B)Line A does not intersect line B. (C)Line A overlaps line B.

Bytelearn · Accepted Answer

Calculate Slope Line A:  Calculate the slope of Line A using the formula (y2 - y1) / (x2 - x1). For points (4,9) and (12,23): Slope of Line A = (23 - 9) / (12 - 4) = 14 / 8 = 1.75. Calculate Slope Line B:  Calculate the slope of Line B using the formula (y2 - y1) / (x2 - x1). For points (0,2) and (-8,-12): Slope of Line B = (-12 - 2) / (-8 - 0) = -14 / -8 = 1.75. Compare Slopes:  Compare the slopes of Line A and Line B. Since both slopes are equal, the lines are either parallel or identical (overlapping). Next, check if they are overlapping by using the point-slope form of a line equation. Point-Slope Form Line A:  Use the point-slope form y - y1 = m(x - x1) for Line A using point (4,9) and slope 1.75: y - 9 = 1.75(x - 4) y = 1.75x - 7 + 9 y = 1.75x + 2. Point-Slope Form Line B:  Use the point-slope form y - y1 = m(x - x1) for Line B using point (0,2) and slope 1.75: y - 2 = 1.75(x - 0) y = 1.75x + 2. Identical Lines:  Since both lines have the same equation y = 1.75x + 2, Line A and Line B are identical, meaning they overlap along their entire length.

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