Equation of a Straight Line in Various Forms

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

Let $ABCD$ be a trapezium where $AB\Vert CD$ and $AB\perp BC$. Suppose the length of the sides $AB$ and $CD$ are $3$ and $5$ units respectively and the coordinate of $B$ and $C$ are $\left(2,5\right)$ and $\left(3,7\right)$ respectively. If $E$ is a point on the side $BC$ and $AE+DE$ is minimum, then the coordinate of $E$ is

The $y$-intercepts of three parallel lines are $2,3,4$, and the sum of their $x$-intercepts is $36$. Then the slope of these three parallel lines is

If the line $px-qy=r$ intersects the coordinate axes at $(a, 0)$ and $(0, b)$ then the value of $(a+b)$ is equal to

If a straight line through the point $P(1, 2),$ which makes an angle $45°$ with the $x$-axis, meets the line $3x+4y+5=0$ at $Q,$ then length of $PQ$ equals units

A straight line $\frac{x}{a}-\frac{y}{b}=1$ passes through the point $(8, 6)$ and cuts a triangle of area $12$ sq. units from the axes of coordinates. The equations of the straight lines are

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

The ratio in which the line joining points $A(-1, -1)$ and $B(2, 1)$ divides the line joining $C(3, 4)$ and $D(1, 2)$

Find the equation of a straight line which passes through the point $(-1, -1)$ and makes an angle $150°$ with positive direction of $x$-axis.

The equation of two equal sides $AB$ and $AC$ of an isosceles triangle $ABC$ are $x+y=5$ and $7x-y=3$ respectively. If the area of the triangle $ABC$ is $5$ sq.units, then the equation of the side $BC$ is

A straight line having slope $\frac{1}{\mathrm{\pi }}$ passes through ordered pairs $\left(\lambda ,\mu \right)$ satisfying the equation ${\cos }^2\mu +4\lambda -{\lambda }^2=5, \mu \in \left[0,\mathrm{\pi }\right]$. The equation of line can be

The angle included between the straight lines $x=0$ and $y=\sqrt{3}x+5$ is _________

The gradient of the straight line which passes through the point $(-3, 6)$ and through the middle point of the line segment joining the points $(4, -5)$ and $(-2, 9)$ is _____

The equation of the straight line which passes through the point $(3, 4)$ and cuts the parts from the coordinate axes, equal in both magnitude and sign is ______

The equation of the straight line which passes through $(0, -4)$ and is inclined to the $x-$axis at an angle $45°$ is ______

The angle made by the straight line $\sqrt{3}x+y=1$ with the negative direction of $x-$axis is ______

If the gradient of the straight line joining the points $(3k, 4)$ and $(4, -3k)$ is $-3,$ then $k=$