2. Lines

Lines

Ex 1.

Write the equation of the line passing through points \(P(1,2)\) and \(Q(3,-1)\) in slope-intercept form and general form.

Ex 2.

Find the parametric equation of the line perpendicular to the line from Ex 1 and passing through point \(R(0,1)\).

Ex 3.

A line passes through point \(A(1, 2)\) and is parallel to the line \(y = 2x + 3\). Find the equation of this line.

Ex 4.

For lines in general form \(l_1: 2x-3y+1=0\) and \(l_2: 4x-6y-5=0\), determine whether they are parallel, perpendicular, or intersect at a single point. If they have a common point, calculate its coordinates.

Ex 5.

Calculate the angle between the line \(y = x + 3\) and the \(Ox\) axis.

Ex 6.

Provide a vector perpendicular to the line \(x + y + 1 = 0\).

Ex 7.

\(\star\) Find the distance of point \(S(2,3)\) from the line \(l: 3x-4y+5=0\).

Ex 8.

\(\star\) Write the equation of the line passing through point \(T(1,1)\) and forming an angle of \(\pi/6\) with the OX axis. Also, provide the intersection point with the OY axis.