Question

The value of k for which the lines x+2y-9=0 and kx+4y+5=0 are parallel, is

Answer 1

Answer:

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Step-by-step explan

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Answer 2

Given,

Two lines with equations x+2y-9=0 and kx+4y+5=0 respectively and both lines are parallel.

To find,

The value of k.

Solution,

• For the two lines to be parallel their slope should be equal.

• The slope of a line with equation ax+by+c=0 is calculated by -a/b.

• Slope of line x + 2y - 9 = 0,

⇒   2y = -x + 9

⇒   y = -x/2 + 9/2.

Therefore the slope of line x + 2y - 9 = 0, is -1/2.

• Slope of line kx + 4y + 5  = 0,

⇒  4y = -kx - 5

⇒  y = -kx/4 - 5/4.

Therefore the slope of line kx + 4y + 5, is -k/4.

Now, since slopes of two lines would be equal

⇒   -1/2 = -k/4

⇒    k = -2

Therefore, The value of k for which the lines x+2y-9=0 and kx+4y+5=0 are parallel is -2.