Various Forms of Equation of a Straight Line

The equation of a straight line passing through the intersection of the lines $x+y+1=0$, $2x-y+5=0$ and through the point $(5,-2)$.

In the gradient-intercept form of equation $y = mx + c$, the point where line cuts $y$-axis is:

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:

Find the equation of a straight line which is parallel to the line $3x-4y=12$ and passes through the point $\left(6,4\right).$

If $3x-4y+7=0$ and $ax+2y+1=0$ are perpendicular, then $\text{'}a\text{'}$ equal to:

If the line $y-\sqrt{3}x+3=0$ cuts the parabola $y^2=x+2$ at $A$ and $B$, then find the value of $PA·PB$. (where, $P\equiv \left(\sqrt{3},0\right)$)

A straight line $AB$ cuts the co-ordinate axes at $A$ and $B.$ If the mid-point of $AB$ is $\left(2,3\right),$ find the equation of $AB.$

If the line $y-\sqrt{3}x+3=0$ cuts the parabola $y^2=x+2$ at $A$ and $B$, then find the value of $PA·PB$. (where, $P\equiv \left(\sqrt{3},0\right)$)

A straight line cuts off the intercepts $OA=a$ and $OB=b$ on the positive direction of $x-$axis and $y-$axis respectively. If the perpendicular from origin to this line makes an angle $\frac{\mathrm{\pi }}{6}$ with positive direction of $y-$axis and are of $∆OAB$ is $\frac{98}{3}\sqrt{3}$ sq. units, then $a^2-b^2$ is equal to

A straight line $\mathrm{AB}$ cuts the co-ordinate axes at $\mathrm{A}$ and $\mathrm{B}$. If the midpoint of $\mathrm{AB}$ is $\left(2, 3\right)$, find the equation of $\mathrm{AB}$.

A straight line $\mathrm{AB}$ cuts the co-ordinate axes at $\mathrm{A}$ and $\mathrm{B}$. If the midpoint of $\mathrm{AB}$ is $\left(2, 3\right)$, find the equation of $\mathrm{AB}$.

Find the slope of the line making inclination of $60°$ with the positive direction of $x$-axis.

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

Show that two lines $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, where $b_1, b_2\ne 0$ are perpendicular if $a_1{a}_2+b_1{b}_2=0$.

Equation of a line is $3x-4y+10=0$. Find its $x$-and $y$-intercepts.

Equation of a line is $3x-4y+10=0$. Find its slope.