What is the equation of the straight line passing through the point 2 3 and making an intercept on the positive y axis?

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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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