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If the straight line 3x-2y plus 3 equals 0 is parallel to KX plus 5Y equals 1 find the value of K?
Zico2010
If two straight lines are parallel, then their gradients must be equal.
In the form y = mx + c, m is the gradient (and c is the intercept with x=0, the y-axis), so rearrange both of these into this form:
3x - 2y +3 = 0 ->
2y = 3x + 3
y = (3/2)x + 3/2
Kx +5y = 1 ->
5y = -Kx +1
y = (-k/5)x +1/5
As the lines are parallel, the gradients must be equal, that is:
3/2 = -k/5
and so k can be found by solving:
k/5 = -3/2
k = 5 x -3 / 2 = -15 / 2 = -7.5
meaning 3x - 2y + 3 = 0 is parallel to -7.5x +5y = 1 (or 5y - 7.5x = 1 writing y first).
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