Find the equation of a straight line which makes acute angle with positive
direction of x–axis, passes through point(–5, 0) and is at a perpendicular
distance of 3 units from origin.

Let the equation of the line be y = mx + c.

As the line passes through (-5, 0), therefore, (-5, 0) must satisfy the equation of the line.

∴0 = m(5) + c

⇒c = -5m

Thus, equation of line is y = mx + m.

Now, the perpendicular distance of the line from origin is 3 units.

As the angle made by the line with positive direction of x-axis is acute,

Thus, equation of the line is

Hope you get this.

Cheers!