Line A passes through the points (0,1) and (8,-2). Line B passes through the points (-8,2) and (16,-7). Which statement is true? Choices: (A)Line A overlaps line B. (B)Line A intersects line B at exactly one point. (C)Line A does not intersect line B.

Question

Line A passes through the points (0,1) and (8,-2). Line B passes through the points (-8,2) and (16,-7). Which statement is true?    Choices: (A)Line A overlaps line B. (B)Line A intersects line B at exactly one point. (C)Line A does not intersect line B.

Bytelearn · Accepted Answer

Calculate slope Line A:  Calculate the slope of Line A using the points (0,1) and (8,-2). Slope formula: (y2 - y1) / (x2 - x1) Slope of Line A = (-2 - 1) / (8 - 0) = -3 / 8 Calculate slope Line B:  Calculate the slope of Line B using the points (-8,2) and (16,-7). Slope formula: (y2 - y1) / (x2 - x1) Slope of Line B = (-7 - 2) / (16 + 8) = -9 / 24 = -3 / 8 Compare slopes:  Compare the slopes of Line A and Line B. Both lines have the same slope of -3/8. Since they have the same slope, they are either parallel or the same line (coincident). Check coincident lines:  Check if the lines are coincident by plugging one point from Line A into the equation of Line B. Equation of Line B from point (-8,2): y - 2 = -3/8(x + 8) Substitute point (0,1) from Line A into this equation: 1 - 2 = -3/8(0 + 8) -1 = -3

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