Question

Show that the equation
lx + my = 1 (l,m not equal to 0)
represents a straight line.​

Answer 1

Given:

An equation

lx + my = 1, where l,m $\not=$ 0

To Find:

The given equation is an equation of a straight line.

Solution:

We know that the equation of a straight line is given by,

y = Mx + C         ......(1)

Where M = slope of the line,

And C = y-intercept i.e. the value of y when x = 0.

The given line is,

lx + my = 1        ......(2)

From equation (2) we get

  ($\bold{\frac{l}{m} }$)x + y = $\bold{\frac{1}{m}}$

⇒  y = -( $\bold{\frac{l}{m} }$)x +$\bold{\frac{1}{m}}$         (since  l,m $\not=$ 0) ......(3)

If we compare equation (3) with equation (1) we get

M = - $\bold{\frac{l}{m} }$

C = +$\bold{\frac{1}{m}}$

i.e. we can write equation (3) in the form of equation (1)

Therefore, the equation  lx + my = 1 (l,m $\not=$ 0)  represents an equation of a straight line.​

Answer 2

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Step-by-step explanation:

it would be helpful