Question

A straight line whose inclination with the positive direction of the x-axis measured in anticlockwise sense is π/3 makes positive intercept on the y-axis. If the straight line is at a distance of 4 from the origin, find its equation.

Answer 1

Please see the attachment

Answer 2

Answer:

Required equation is y = √3x + 4.

Step-by-step explanation:

Given:

Line makes π/3 angle with positive direction of x-axis measured anti-clockwise.

Line also make positive intercept on y-axis.

line is at distance of 4 unit from origin.

To find: Equation of line.

We use Slope-intercept form to write the equation.

y = mx + c where m is slope of line and c is y-intercept.

here, $m=tan\,\theta=tan\,\frac{\pi}{3}=\sqrt{3}$

y-intercept = 4   ⇒ c = 4

Thus, Equation is  y = √3x + 4

Therefore, Required equation is y = √3x + 4.