# SOLUTION: The line joining (-2,1) to (6,4), is parallel to the line joining (-q,5) to (4,q). Find the value of q. It would certainly be a great pleasure for me if you solve my question.

Algebra ->  Algebra  -> Coordinate-system -> SOLUTION: The line joining (-2,1) to (6,4), is parallel to the line joining (-q,5) to (4,q). Find the value of q. It would certainly be a great pleasure for me if you solve my question.       Log On

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 Question 206576This question is from textbook Longman mathematics for IGCSE Book1 : The line joining (-2,1) to (6,4), is parallel to the line joining (-q,5) to (4,q). Find the value of q. It would certainly be a great pleasure for me if you solve my question. Thank you very much indeed.This question is from textbook Longman mathematics for IGCSE Book1 Found 2 solutions by nerdybill, Theo:Answer by nerdybill(6963)   (Show Source): You can put this solution on YOUR website!The line joining (-2,1) to (6,4), is parallel to the line joining (-q,5) to (4,q). Find the value of q. . First, find the slope of line:(-2,1) to (6,4) m = (4-1)/(6-(-2)) m = 3/(6+2) m = 3/8 . Slope of our new line: (-q,5) and (4,q) m = (q-5)/(4-(-q)) m = (q-5)/(4+q) . Slopes must be equal if they are parallel so set the two equations equal to each other: 3/8 = (q-5)/(4+q) 3(4+q) = 8(q-5) 12+3q = 8q-40 12 = 5q-40 52 = 5q 52/5 = q Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!if the lines are parallel then their slopes have to be equal. ----- your slope is given by the equation (y2-y1)/(x2-x1) ----- your first line joins (-2,1) to (6,4) y2 - y1 = 4 - 1 = 3 x2 - x1 = 6 - (-2) = 8 ----- the slope of your first line is 3/8 ----- your second line joins (-q,5) to (4,q) for the slopes to be equal, y2-y1 / x2-x1 must equal 3/8 ----- y2-y1 = q-5 x2-x1 = 4-(-q) = q + 4 ----- (q-5)/(q+4) must equal 3/8 ----- if we multiply both sides of this equation by 8 we get: (8q-40)/(q+4) = 3 ----- if we multiply both sides of this equation by (q+4) we get: 8q-40 = 3q + 12 ----- if we subtract 3q from both sides of this equation and we add 40 to both sides of this equation we get: 5q = 52 ----- if we divide both sides of this equation by 5 we get: q = (52/5) this is equivalent to 10.4 ----- our first line passes through the points (-2,1) and (6,4) our second line passes through the points (-10.4,5) and (4,10.4) ----- if both lines have the same slope, then the slope of the second line should equal (3/8) ----- the slope of the second line is y2-y1/x2-x1 = (10.4 - 5)/(4 - (-10.4)) this comes out to be 5.4/14.4 ----- 5.4/14.4 is the same ratio as 3/8 so the slopes are the same. ----- our answer is q = 10.4 ---- to graph these equations, we need to get them into the standard form of y = mx + b ----- m is the slope = 3/8 b is the y intercept which is the value of y when x = 0 ----- to find b, we substitute one of the points in the equation and solve for b. ----- for the first equation, we will use the point (6,4) y = mx + b becomes 4 = 6*(3/8) + b this makes b = 1.75 ----- standard form of our first equation is y = (3/8)*x + 1.75 ----- for the second equation, we will use the point (4,10.4) y = mx + b becomes 10.4 = 4*(3/8) + b this makes b = 8.9 ----- standard form of our second equation is y = (3/8)*x + 8.9 ----- graph of both equations looks like the following: -----