Question

Equation of another line parallel to the line represented by 2x − 6y = 7 is ______.

Options

• y = 3x − 7

• 2x = 9 − 6y

• x − 3y = 7

• `x = 7/2 - 3y`

Answer 1

Equation of another line parallel to the line represented by 2x − 6y = 7 is x − 3y = 7.

Explanation:

2x − 6y = 7

`x − 3y = 7/2`    ...(Both side divide by 2)

We rewrite it in the slope-intercept form, y = mx + c

`− 3y = −x + 7/2`

y = `1/3x - 7/6`

Parallel lines must have the same slope `1/3`.

So any parallel line will be:

y = `1/3x + c`

3y = x + 3c   ...(Both side multiply by 3)

x − 3y = −3c

So general form of a parallel line:

x − 3y = k

Taking k = 7(which is different from `7/2`)

x − 3y = 7