Question

Two lines are given to be parallel. The equation of one of these lines is 5x - 3y = 2, The equation of the second line can be ______.

पर्याय

• -15x - 9y = 5

• 15x + 9y = 5

• 9x - 15y = 6

• -15x + 9y = 5

Answer 1

Two lines are given to be parallel. The equation of one of these lines is 5x - 3y = 2, The equation of the second line can be -15x - 9y = 5.

Explanation:

For two lines to be parallel, their slopes must be equal. The slope of a line given by the equation  Ax + By = C is `-A/B`.

 Let's find the slope of the given line and compare it with the options to identify the parallel line.

The given equation of the first line is:

5x - 3y = 2

Rearranging it in the slope-intercept form y = mx + b, where m is the slope:

-3y = -5x + 2

`y =5/3x - 2/3`

 The slope of this line is `5/3`

∴ The equation of the second line is -15x - 9y = 5

`y = -15/(-9)x  - 5/(-9) `

which simplifies to `y = 5/3x + 5/9` where the slope is `5/3`