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10 Questions 10 Marks 10 Mins
Concept:
Line: Line in slope form is given as,
\(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} = 1\)
where a is x-intercept and b is y-intercept.
Calculation:
Let the equation of line be \(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} = 1\) ----(1)
Where a is x-intercept and b is y-intercept.
The line is passing through (2,3). So, (2,3) should satisfy the equation of line.
Put x = 2 & y = 3 in equation (1)
\(\frac{2}{{\rm{a}}} + \frac{3}{{\rm{b}}} = 1\) ----(2)
Now, we have given that the intercept on the positive y-axis equal to twice its intercept on the positive x-axis.
So, b = 2a
Put b = 2a in equation 2
\(\frac{2}{{\rm{a}}} + \frac{3}{{2{\rm{a}}}} = 1\)
⇒ 2 + 3/2 = a
⇒ a = 7/2
Now, b = 2a = 7
So, equation of line will be,
\(\frac{{\rm{x}}}{{\frac{7}{2}}} + \frac{{\rm{y}}}{7} = 1\)
⇒ 2x + y = 7
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