Various Forms of the Equation of a Line

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

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 $AB.$

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 $\mathrm{AB}$.

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.

The slope of a line joining the points $\left(2,k\right)$ and $\left(-4,2\right)$ is $\frac{1}{2},$ then find $\text{'}k\text{'}.$

The equation of right bisector of the line joining the points $(1,1)$ and $(3,5)$ is

Let $P=(-1,0),Q=(0,0) \text{and} R=(3,3\sqrt{3})$ be three points then the equation of bisector of the angle $PQR$ is$?$

A straight line $L,$ whose slope is $m,$ passes through the point $\left(2,0\right)$ and intersects $y^2-4x+4=0$ in distinct points. Hence $m$ lies in the interval

Find the equation of line at which the length of the perpendicular from the origin is $2$ and the slope of this perpendicular is $\frac{5}{12}.$

Let a line $AB$ cuts an intercept of $7$ units and $\frac{7}{3}$ units on positive sides of axes. Find the number of integral values of $m$ so that the $x-$coordinate of the point of intersection of lines $mx+y=3$ and $AB$ is also an integer.

The angle between the lines $x-\sqrt{3}y+5=0$ and $y$-axis is

A line is such that its segment between the lines $5x-y+4=0$ and $3x+4y-4=0$ is bisected at the point $\left(1, 5\right)$. Obtain its equation.

Find the equation of a line perpendicular to the line $x-2y+3=0$ and passing through the point $\left(1, -2\right)$.

Reduce the equation $\sqrt{3}x+y-8=0$ into normal form. Find the values of $p$ and $\omega$.

Find the equation of the line whose perpendicular distance from the origin is $4$ units and the angle which the normal makes with positive direction of $x$-axis is $15°$.

The Fahrenheit temperature $F$ and absolute temperature $K$ satisfy a linear equation. Given that $K=273$ when $F=32$ and that $K=373$ when $F=212$. Express $K$ in terms of $F$ and find the value of $F$, when $K=0$.