2.8

Write the equation of the line for which $\tan \theta =\frac{1}{2}$, where $\theta$ is the inclination of the line and $x$-intercept $4$.

Find the values of $k$ for which the line $\left(k-3\right)x-\left(4-k^2\right)y+k^2-7k+6=0$ is parallel to the $y$-axis.

Find the equation of the straight line parallel to $x+2y=3$ and passing through the point$\left(3,4\right)$ .

Find the equation of the line through $\left(-2,3\right)$ parallel to the line $3x-4y+2=0$

Find the equation of the line through $\left(-2,-1\right)$ and parallel to line $x=0$.

The equation of two sides of a square whose area is $25$ square units are $3x-4y=0$ and $4x+3y=0.$ Find the equation of the other two sides of the square. Give all possible answers.

The equation of one side of a rectangle is $3x-4y-10=0$ and the coordinates of two of its vertices are $\left(-2,1\right)$ and $\left(2,4\right)$. Find the area of the rectangle and the equation of that diagonal of the rectangle which passes through the point $\left(2,4\right)$.

Sides of a square lie on the line $5x-12y-65=0$ and $5x-12y+26=0$. Find the area of the square.