Question

Equation of the line parallel to 2x + 3y = 8 is [ ]

a) 3x + 2y = 7 b) 3x – 2y = 4 c) 2x + 3y = – 9 d) x + y = 2.​

Answer 1

Hope this helps you. .

- Khushali.S.S. .

Answer 2

Answer:

$\large\boxed{\sf{(c)\;2x+3y=-9}}$

Step-by-step explanation:

Given the equation of a line such that,

$2x + 3y = 8$

Now, we have to find the equation of a line parallel to the given line.

For this, we have to find the slope of given line.

Therefore, differentiating the eqn, we get,

$= > 2 \times 1 + 3 \dfrac{dy}{dx} = 0 \\ \\ = > 3 \dfrac{dy}{dx} = - 2 \\ \\ = > \dfrac{dy}{dx} = - \frac{2}{3}$

Therefore, slope of given line = $\bold{-\dfrac{2}{3}}$

Now, we know that, parallel lines have same slope.

Therefore, the required line will also have slope equals to $-\dfrac{2}{3}$.

On observation and calculation, only option (c) seems to satisfy the required condition.

Let's find the slope of (c) 2x + 3y = -9

Differentiating both sides wrt x ,we get,

$= > 2 \times 1 + 3 \dfrac{dy}{dx} = 0 \\ \\ = >2 + 3 \dfrac{dy}{dx} = 0 \\ \\ = > \dfrac{dy}{dx} = - \frac{2}{3}$

Therefore, this line also has slope $\bold{-\dfrac{2}{3}}$

Therefore, this line is parallel to the given line.

Hence, correct option is (c) 2x + 3y = -9