Question

If line y = mc + c and 4x- y + 3 = 0 mutually perpendicular to each other . Find the value of m

Answer 1

$\bf{\underline{Question:-}}$

If line y = mc + c and 4x- y + 3 = 0 mutually perpendicular to each other . Find the value of m.

$\bf{\underline{Solution:-}}$

→ The given line are = y = mx + c

And 4x - y + 3 = 0

→ The gradient of 1st line , $\sf m_1 = m$

and the gradient of 2nd line , $\sf m_2 = 4$

Given that both line are perpendicular to each other

So,

$\rm→ m_1 × m_2 = - 1$

$\rm→ m × 4 = - 1$

$\rm → m = \large\frac{-1}{4}$

$\bf{\underline{Hence:-}}$

$\bf\huge m = -\frac{1}{4}$

Answer 2

Answer:

Given:

The equations ,

y=mx+c and 4x-y+3=0 are mutually perpendicular to each other.

To find:

The value of m

Solution:

As we know that,

Slope of the line,

ax+by+c=0 is m=-a/b

Now,

Slope of the line mx-y+c=0 is

m1=-(m)/-1=m

Slope of the line,4x-y+3=0 is

m2=-(4)/-1=4

Since, The lines are mutually perpendicular to each other,

So,

$m1 \times m2 = - 1 \\ 4m = - 1 \\ m = - 1 \div 4$

Hence the value of m is -1/4.

Step-by-step explanation:

Hope it helps you........