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