Question

What is the value of b that makes the lines, given by 3x-y=4 and 2y+4bx=1, perpendicular?

Answer 1

b = 1/6

Explanation:

3x-y=4 ...1st equation

Rewriting in slope- intercept form:

y = 3x - 4

2y+4bx=1

Rewriting in slope- intercept form:

2y = -4bx + 1

y = -4bx/2 + 1/2

Equation of line: y = mx + c

where m = slope, c = intercept

For a line to be perpendicular to another, the slope of one will be the negative reciprocal of the slope of another.

Slope of the 1st equation = 3

m = 3

reciprocal of 3 = 1/3

negative reciprocal of 3 = -1/3

Slope of the 2nd equation = -4b/2

we equate both slope:

negative reciprocal of 3 = -4b/2

-1/3 = -4b/2

cross multiply:

-1(2) = 3(-4b)

-2 = -12b

Divide both sides by -12:

-2/-12 = -12b/-12

b = 1/6

Hence, the value of b that makes the lines perpendicular is 1/6