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### High School Mathematics - 29.11 The Two Points Form of A Line

 Equation of a line passing through the points A(x1 , y1) and B(x2 , y2) is (x - x1) (y2 - y1) = (y - y1) (x2 - x1). Example: Find the equation of line passing through (3,4) and (5,6). Solution: Formula for finding the equation of line when two points are given is (x - x1) (y2 - y1) = (y - y1) (x2 - x1). Given that, (x1 , y1) = (3,4) (x2 , y2) = (5,6) Substituting these values in the formula, we get (x - 3) (6 - 4) = (y - 4) (5 - 3) (x - 3) 2 = (y - 4) 2 2x - 6 = 2y - 8 2x - 2y + 2 = 0 Therefore, the 2x - 2y + 2 = 0 is the required line. Directions: Find the equation of the line, given two points. Also write at least 10 examples of your own.
 Q 1: Find the equation of line passing through (4,5) and (2,6).2x - y - 6 = 0x - y - 3 = 0x - y + 3 = 0x - 2y + 6 = 0 Q 2: Find the equation of line passing through (-2,1) and (3,4).3y - 5x + 7 = 05x - 3y + 7 = 03x - 5y + 7 = 05x - 3y - 7 = 0 Q 3: Find the equation of line passing through (-2,3) and (4,5).2x - 6y + 6 = 02y - 6x + 6 = 0None of these6x - 2y + 6 = 0 Q 4: Find the equation of line passing through (5,6) and (4,5).-x + y - 1 = 0x + y + 1 = 0x - y + 1 = 0x + y - 1 = 0 Q 5: Find the equation of line passing through (0,0) and (1,3).3x - y = 0None of these3x + y = 03x - y + 3 = 0 Q 6: Find the equation of line passing through (3,4) and (-5,1).8x + 3y + 23 = 03x + 8y + 23 = 08x - 3y + 23 = 03x - 8y + 23 = 0 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!