Question

The equation of the line which passes through the point of intersection of lines \(x+2y+6=0\), \(2x-y=2\) and which makes intercept 5 on Y - axis is

• A. \(39x-2y+10=0\)
• B. \(39x+2y+10=0\)
• C. \(39x+2y-10=0\)
• D. \(39x-2y-10=0\)

Hint:

Find the intersection point, then use it together with the point (0, 5) to find the line.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A y-intercept of 5 means the line passes through \((0,5)\).

Step 2: Intersection point
From \(2x-y=2\), \(y=2x-2\). Substitute in \(x+2y+6=0\): \(x+4x-4+6=0\), hence \(x=-\frac{2}{5}\), \(y=-\frac{14}{5}\).

Step 3: Find the line
Slope \(=\dfrac{5+\frac{14}{5}}{0+\frac{2}{5}}=\dfrac{39/5}{2/5}=\dfrac{39}{2}\)
\(y=\dfrac{39}{2}x+5\), so \(39x-2y+10=0\).

Step 4: Compare the options
This is the first option.

Final Answer:
The line is 39x - 2y + 10 = 0. \[ \boxed{\text{(A) }39x-2y+10=0} \]