The equation of the straight line whose intercepts on x axis and y axis are respectively twice and thrice of those by the line 3x + 4y = 12 is :-9x + 8y = 729x – 8y = 728x + 9y = 72None of these

The equation of a line in intercept form is given by x/a + y/b = 1, where a and b are the x-intercept and y-intercept respectively.

Given the equation of the line is 3x + 4y = 12, we can rewrite this in intercept form to find the intercepts:

x/(12/3) + y/(12/4) = 1 x/4 + y/3 = 1

So, the x-intercept is 4 and the y-intercept is 3.

The problem states that the intercepts on the x-axis and y-axis are respectively twice and thrice of those by the given line. So, the x-intercept of the new line is 24 = 8 and the y-intercept is 33 = 9.

Substituting these values into the intercept form of the equation gives:

x/8 + y/9 = 1

Multiplying through by 72 to clear the fractions gives:

9x + 8y = 72

So, the equation of the line is 9x + 8y = 72.