Coordinate Geometry : Equation of a straight line

Question

What is the equation of the line that is parallel to the line 3x + 7y = 10 and passes through the point (4, 8)?

1. 7x – 3y = 46
2. 3x + 7y = 44
3. 9x + 21y – 184 = 0
4. 3x + 7y = 68
   
   

Correct Choice is (4) and Correct Answer 3x + 7y = 68

Explanatory Answer

Note: If two lines are parallel, then their slopes will be the same.

Therefore, if two lines are parallel and the equation of one of the lines is a₁x + b₁y = c₁, then the equation of the line parallel to the line will be of the form a₁x + b₁y = c₂

In this example, the equation of the first line is 3x + 7y = 10
So, the second line will have a generalized equation of the form 3x + 7y = k.

As, the second line passes through the point (4, 8), substituting x = 4 and y = 8 should satisfy the equation of the line.

i.e. 3(4) + 7(8) = k

12 + 56 + = k 0

=> k = 68

Hence, the equation of the line 3x + 7y = 68

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