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

Answer 1

The Correct Option is A

Explanation:
Concept:The equation of line is y = mx + c, where m is slope.Given equation of line is x - y = 4$\Rightarrow y=x-4$ which is equal to $y=mx+c$, where $m$ is slope of the line$\Rightarrow m=1$$\Rightarrow m=\tan \theta =1$$\Rightarrow \theta ={45}^{\circ }$So, the equation of line $x-y=4$ makes angle ${\theta }_1={45}^{\circ }$ with $X$-axis.The required line makes an angle ${\theta }_2={45}^{\circ }$ with Y-axis. and makes an angle ${45}^{\circ }$ with $X$-axis also.The line passing through the point $(0,1)$.Slope of the required line is $m=\tan \theta =1$Equation 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).