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If the graphs of the lines 2x -5y=7 and 10x+by=7

are perpendicular, what is the value of b?

User Andreis
by
7.8k points

1 Answer

4 votes

Answer: b = 4

Explanation:

If the slope of a line is m, the slope of the perpendicular line would be the negative reciprocal i.e. -1/m

So let's find the slope of 2x-5y = 7.

2x - 5y = 7 (subtract 5y on both sides)

2x = 7 + 5y (subtract 7 on both sides)

2x - 7 = 5y (divide by 5 on both sides)

2/5 x - 7/5 = y OR y = 2/5x - 7/5

Therefore, the slope of 2x-5y = 7 is 2/5.

The perpendicular line will therefore have a slope of -5/2

Once we rearrange the second line 10x + by = 7

We end up with:

by = 7 - 10x

y = 7/b - 10/bx

So we set:

-10/b = -5/2

10 = 5b/2

20 = 5b

20/5 = b --> b=4

User Nick Van Brunt
by
8.8k points

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