Equation of a Straight Line in Various Forms

The straight-line equation$y=\frac{x}{3}+\frac{1}{4}$ cuts $y$- axis at the point

The equation of the image of the line $x+2=0$ with respect to $x=0$ is

If a line passes through point $A(0,c)$ and has gradient $\text{'}m\text{'}$ then the equation will be:

If the straight line drawn through the point $P\left(\sqrt{3}\text{, }2\right)$  and inclined at an angle $\frac{\pi }{6}$ with the $x-$axis meets the line $\sqrt{3}x-4y+8=0$ at $Q$ Find the length $PQ$.

Use concept of slope to prove following points are collinear.

$\left(0,2\right),\left(1,5\right),\left(-2,-4\right) \& \left(-6,-16\right)$

Use concept of slope to prove following points are collinear.

$\left(4,2\right),\left(5,4\right),\left(2,-2\right) \& \left(3,0\right)$

Use concept of slope to prove following points are collinear.

$\left(4,8\right),\left(5,12\right),\left(9,28\right) \& \left(11,36\right)$

The equations of sides $\overline{AB}, \overline{BC}$ and $\overline{CA}$ of a triangle $ABC$ are $2x+y=0, x+py=q$ and $x-y=3$ respectively. If $P(2, 3)$ is its orthocenter, then the value of $p+q$ equals

Use concept of slope to prove following points are collinear.

$\left(5,-2\right),\left(4,-1\right),\left(1,2\right) \& \left(3,0\right)$

Use concept of slope to prove following points are collinear.

$\left(0,2\right),\left(1,5\right),\left(-2,-4\right) \& \left(-6,-16\right)$

Use concept of slope to prove following points are collinear.

$\left(4,2\right),\left(5,4\right),\left(2,-2\right) \& \left(3,0\right)$

Use concept of slope to prove following points are collinear.

$\left(4,8\right),\left(5,12\right),\left(9,28\right) \& \left(11,36\right)$

Use concept of slope to prove following points are collinear.

$\left(0,3\right),\left(1,5\right),\left(-2,-1\right) \& \left(-4,-5\right)$

In the $xy$-plane, how many straight lines whose $x$-intercept is a prime number and whose $y$-intercept is a positive integer pass through the point $(4, 3)$?

The equation $y=\pm \sqrt{3}x, y=1$ are the sides of

The equation of a plane which passes through $\left(2,-3, 1\right)$ and is normal to the line joining the points $\left(3,4,-1\right)$ and $\left(2,-1,5\right)$ is given by

If the points $\left(1,0\right),\left(0,1\right)$ and $\left(x,8\right)$ are collinear, then the value of $x$ is equal to