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.

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(7384) (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(13342) (Show Source): You can put this solution on YOUR website!
if the lines are parallel then their slopes have to be equal.
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your slope is given by the equation (y2-y1)/(x2-x1)
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your first line joins (-2,1) to (6,4)
y2 - y1 = 4 - 1 = 3
x2 - x1 = 6 - (-2) = 8
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the slope of your first line is 3/8
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your second line joins (-q,5) to (4,q)
for the slopes to be equal, y2-y1 / x2-x1 must equal 3/8
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y2-y1 = q-5
x2-x1 = 4-(-q) = q + 4
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(q-5)/(q+4) must equal 3/8
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if we multiply both sides of this equation by 8 we get:
(8q-40)/(q+4) = 3
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if we multiply both sides of this equation by (q+4) we get:
8q-40 = 3q + 12
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if we subtract 3q from both sides of this equation and we add 40 to both sides of this equation we get:
5q = 52
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if we divide both sides of this equation by 5 we get:
q = (52/5)
this is equivalent to 10.4
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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)
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if both lines have the same slope, then the slope of the second line should equal (3/8)
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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
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5.4/14.4 is the same ratio as 3/8 so the slopes are the same.
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our answer is q = 10.4
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to graph these equations, we need to get them into the standard form of y = mx + b
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m is the slope = 3/8
b is the y intercept which is the value of y when x = 0
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to find b, we substitute one of the points in the equation and solve for b.
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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
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standard form of our first equation is y = (3/8)*x + 1.75
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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
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standard form of our second equation is y = (3/8)*x + 8.9
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graph of both equations looks like the following:

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