Coordinate Geometry : Equation of a straight line

Question

From the following choices what is the equation of a line whose x intercept is half as that of the line 3x + 4y = 12 and y intercept is twice as that of the same line.

1. 3x + 8y = 24
2. 8x + 3y = 24
3. 16x + 3y = 24
4. 3x + y = 6
   
   

Correct Choice is (4) and Correct Answer 3x + y = 6

Explanatory Answer

Note: To find x intercept in a given equation put y = 0 in that equation and find the value for x (i.e., x-intercept).

Put y = 0 to find the x-intercept in 3x + 4y = 12, i.e., 3x + 4(0) = 12, therefore, x-intercept = 12/3 = 4.

Similarly, to find y intercept in a given equation put x = 0 in that equation and find the value for y (i.e., y-intercept).

Substituting x = 0 to find the y-intercept in 3x + 4y = 12, i.e., 3(0) + 4y = 12, therefore, y-intercept = 12/4 = 3

For the equation under question, the x-intercept is half of the x-intercept of the line 3x + 4y = 12 and is equal to 2
And the y intercept of the new line is twice the y-intercept of 3x + 4y = 12 and is equal to 6.

Now the equation of a line whose x-intercept and y-intercept is given can be written as .

Therefore, equation of the line whose x-intercept is 2 and y-intercept is 6 is .

It can be rewritten as 3x + y = 6.

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