Question

please help I am reposting this question.

Answer 1

Answer:

b = -9

Step-by-step explanation:

According to the given question,

The line passes through (-2,3) and (4,b) and it is perpendicular to 2x-4y=5

And we are asked to find, value of b.

So, We know equation of a line which passes through two given points is,

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

So by putting the values,

• (y-3)/(b-3) = (x+2)/(4+2)

• 6(y-3) = (x+2)(b-3)

• After simplification we get,

• 6y+x(3-b) = 2(b+6)

Now we have to find slope of the tangent,

which is "m"

So, 6y = -(3-b)x + 2(b+6)

or, y = [(b-3)x]/6 + (b+6)/3

So on comparing with y = mx+c

we get m = (b-3)/6

And also m1 which is slope of 2x-4y=5 is,

• 2x-5 = 4y

• 4y = 2x-5

• y = x/2 - 5/4

So, again comparing with general equation i.e., y = mx+c

we get m1 = 1/2

Hence, We know both lines are perpendicular so; m×m1 = -1

Therefore, (b-3)/6 × 1/2 = -1

After simplify,

b = -9 ans.