The value of x if lines PQ and RS are parallel is: x = 9.
<h3>What is the Slope of Parallel Lines?</h3>
The slope values of two lines that are parallel to each other are always the same.
Slope = change in y/change in x
Thus, since PQ and RS are parallel to each other, therefore, their slope will be equal.
Given:
P(x,4)
Q(3,2)
R(-1,5)
S(2,4)
Slope of PQ = Slope of RS
(4 - 2)/(3 - x) = (5 - 4)/(-1 - 2)
2/(3 - x) = 1/-3
Cross multiply
(2)(-3) = (1)(3 - x)
-6 = 3 - x
-6 - 3 = -x
-9 = -x
9 = x
x = 9
Therefore, the value of x if lines PQ and RS are parallel is: x = 9.
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