Then use any of the two equations to find aįind the equation of a line L 1 that passes through the point (2, 1) and is parallel to the line L 2 through the points (-1, 2) and (3, 4). Substitute a by 3 b - 6 in the equation 8 - b = 16 - 2 a to obtain We now solve the system of the two equations in a and b obtained above and given by Slope of segment AD = (b - 2) / (a - 0) = (b - 2) / aįor the segments BC and AD to be parallel, their slopes must be equal Slope of segment AB = (6 - 2) / (2 - 0) = 2įor the segments AB and DC to be parallel, their slopes must be equal, hence the equation For the points A, B, C and D to be the vertices of a parallelogram, segment AB must be parallel to segment DC and segment BC must be parallel to segment AD as shown in the figure below. Let (a, b) be the coordinates of point D. The two lines are parallel, hence their slopes are equalįind the coordinate of point D so that the points A(0, 2), B(2,6), C(8, 8) and D are the vertices of a parallelogram. The two lines are parallel and therefore their slopes are equal henceįind a so that the line through the points (1, 2) and (0, 3) and the line through the points (a, 2) and ( -2, 7) are parallel.įind the slope m 1 through the points (1, 2) and (0, 3)įind the slope m 2 through the points (a, 2) and (-2, 7) Solve for y and find the slope of each lineĦ k x - 3 y = 9, solve for y, y = 2 k x - 3, slope = 2 k The lines with equal slopes are the lines given in parts a) b) and d) and they are therefore parallel.įind k so that the lines with equations 6 k x - 3 y = 9 and - 4 x + 5 y = 7 are parallel. We first need to write each line in slope intercept form y = m x + b and find its slope m.ī) 2 x - y = 2, solve for y, y = 2 x - 2, slope = 2Ĭ) - 4 y + 2 x = 0, solve for y, y = (1 / 2) x, slope = 1 / 2ĭ) - 4 y + 8 x = 9, solve for y, y = 2 x - 9 / 4, slope = 2 Which of the lines given by the equationsĪ) y = 2 x - 3 b) 2 x - y = 2 c) - 4 y + 2 x = 0 d) - 4 y + 8 x = 9
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