Question

two lines a1x+b1y+c1=0 and a2x+b2y+c2=0 are parallel if​

Answer 1

Answer:

they are parallel if a1/a2 = b1/b2 is not equal to c1/c2

Step-by-step explanation:

it is the condition for parallel lines

Answer 2

Given:

Equation of two lines, $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$.

To Find:

The condition for which two lines are parallel.

Solution:

Convert the equation $a_1x+b_1y+c_1=0$ for y in terms of x.

$b_1y=-a_1x-c_1\\y=\frac{-a_1x-c_1}{b_1} \\=\frac{-a_1}{b_1}x-\frac{c_1}{b_1}$

Here, for the line $a_1x+b_1y+c_1=0$, the slope is $\frac{-a_1}{b_1}$ and the x-intercept is $\frac{-c_1}{b_1}$.

Convert the equation $a_2x+b_2y+c_2=0$ for y in terms of x.

$b_2y=-a_2x-c_2\\y=\frac{-a_2x-c_2}{b_2}\\ =\frac{-a_2}{b_2}x-\frac{c_2}{b_2}$

Here, for the line $a_2x+b_2y+c_2=0$, the slope is $\frac{-a_2}{b_2}$and the x-intercept is $\frac{-c_2}{b_2}$.

For two lines to be parallel, their slopes are equal.

$-\frac{a_1}{b_1}=-\frac{a_2}{b_2}\\ \frac{a_1}{b_1}=\frac{a_2}{b_2}$

Thus, for $\frac{a_1}{b_1}=\frac{a_2}{b_2}$ the two lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ are parallel.