Which of the following equations represents a line that is parallel to the line represented by 3x + 5y = –3? a. 3x + 5y = 2 b. 6x + 10y = –6 c. –5x + 3y = 2 d. –3x + 5y = –3

Option b  

The equation 6x + 10y = -6 represents a line that is parallel to the line 3x + 5y = –3

Solution:

let us consider two equations

If two equations are parallel to each other,then the condition is  

------------- eqn 1

From question, given that 3x + 5y = –3

Hence we get,

Applying equation 1 in the given options,

Case 1:  

Consider option 1, given that 3x + 5y = 2

Hence we get,

By using equation 1,

Hence the condition is not satisfied.  

Case 2:  

Consider option 2, given that 6x + 10y = –6

Hence we get,

By using equation 1,

By simplifying we get,

Hence the condition is satisfied. So, 6x + 10y = –6 represents the line which is parallel to 3x + 5y = –3

Case 3:

Consider option 3, given that -5x + 3y = –2

Hence we get,

By using equation 1,

Hence the condition is not satisfied.

Case 4:

Consider option 4, given that –3x + 5y = –3

Hence we get

By using equation 1,

Hence the condition is not satisfied.

Thus the correct answer is option b