Line m passes through the points (4, 1) and (7, 3) while line n passes through the points (-3, 5) and (-9, 1).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are perpendicular.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 parallel.D.Lines m and n have opposite reciprocal slopes so they are parallel.SUBMITarrow_backPREVIOUS
Question
Line m passes through the points (4, 1) and (7, 3) while line n passes through the points (-3, 5) and (-9, 1).Which statement accurately describes the relationship between the two lines?A.Lines m and n have the same slope so they are perpendicular.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 parallel.D.Lines m and n have opposite reciprocal slopes so they are parallel.SUBMITarrow_backPREVIOUS
Solution
To answer this question, we first need to calculate 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, which passes through the points (4, 1) and (7, 3), the slope (m1) can be calculated as follows:
m1 = (3 - 1) / (7 - 4) = 2 / 3
For line n, which passes through the points (-3, 5) and (-9, 1), the slope (m2) can be calculated as follows:
m2 = (1 - 5) / (-9 - (-3)) = -4 / -6 = 2 / 3
As we can see, lines m and n have the same slope (2/3). Therefore, they are parallel. So, the correct answer is:
C. Lines m and n have the same slope so they are parallel.
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