Question

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Find k if the lines 3x-5y=9 & 2x+ky=11 are a)parallel and b)perpendicular

Answer 1

3x - 5y = 9
2x + ky = 11
Express the equations in the form of y = mx + c, where m is the gradient and c is the y-intercept.
a)
3x - 5y = 9
5y = 3x - 9
y = 3x / 5 - 9 / 5
2x + ky = 11
ky = -2x + 11
y = -2x / k + 11 / k
Since the lines are parallel, the gradient are the same.
3 / 5 = -2 / k
k = -2 / (3 / 5) = -10 / 3
b)
Now, the lines are perpendicular, which means the gradients are the negative reciprocals of each other.
3 / 5 = -1 / (-2 / k) = k / 2
k = 6 / 5