Question

What is the equation of line passing through (0, 1) and making an angle with the y-axis equal to the inclination of the line x - y = 4 with x-axis?

• A. (A) y = x + 1
• B. (B) x = y + 1
• C. (C) 2x = y + 2
• D. (D) 2x = y - 2

Answer 1

Answer: (A)

(A) y = x + 1

Answer 2

Explanation:
Concept:The equation of line is y = mx + c, where m is slope.Given equation of line is x - y = 4⇒y=x−4 which is equal to y=mx+c, where m is slope of the line⇒m=1⇒m=tan⁡θ=1⇒θ=45∘So, the equation of line x−y=4 makes angle θ1=45∘ with X-axis.The required line makes an angle θ2=45∘ with Y-axis. and makes an angle 45∘ with X-axis also.The line passing through the point (0,1).Slope of the required line is m=tan⁡θ=1Equation of line is, y = mx+c⇒ y = x + c.Since, the line passing through the point (0,1) ,put x = 0 and y = 1 to find c.⇒ 1 = 0 + c⇒ c = 1.Equation of line is y = x + 1Hence, the equation of line passing through (0, 1) and making an angle with the y-axis equal to the inclination of the line x - y = 4 with x-axis is y = x + 1.Hence, the correct option is (A).