Line m passes through the points (3, 7) and (6, 12) while line n passes through the points (-5, 1) and (-2, 6).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are parallel.B.Lines m and n have opposite reciprocal slopes so they are perpendicular.C.Lines m and n have the same slope so they are perpendicular.D.Lines m and n have opposite reciprocal slopes so they are parallel.
Question
Line m passes through the points (3, 7) and (6, 12) while line n passes through the points (-5, 1) and (-2, 6).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are parallel.B.Lines m and n have opposite reciprocal slopes so they are perpendicular.C.Lines m and n have the same slope so they are perpendicular.D.Lines m and n have opposite reciprocal slopes so they are parallel.
Solution
First, we need to find the slopes of lines m and n.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).
For line m, the points are (3, 7) and (6, 12). So, the slope of line m is (12 - 7) / (6 - 3) = 5 / 3 = 1.67 (approximately).
For line n, the points are (-5, 1) and (-2, 6). So, the slope of line n is (6 - 1) / (-2 - (-5)) = 5 / 3 = 1.67 (approximately).
So, lines m and n have the same slope.
Therefore, the correct statement is:
A. Lines m and n have the same slope so they are parallel.
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