Conditions for Two Lines to be Parallel and Perpendicular

The line through $P\left(5, 3\right)$ intersects Y-axis at $Q$. Find the coordinates of $Q$.

If the lines $3(\alpha -1)y-6x=2$ and $4y-8x+10=0$ are parallel, then find the value of $\alpha$.

Given equation of line $L_1$ is $y=4$.

Write the slope of line $L_2$, if $L_2$ is bisector of $\angle O$.

The line passing through $A\left(-2, 3\right)$ and $B\left(4, b\right)$ is perpendicular to the line  $2x-4y=5$. Find the value of $b$.

The line through $P\left(5, 3\right)$ intersects $Y-\mathrm{axis}$ at $Q$.

Write the slope of the line.

The slope of a line joining $P\left(6, k\right)$ and $Q(1-3k, 3)$ is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$. Find $k$.

A line $AB$ meets $X-\mathrm{axis}$ at $A$ and $Y-\mathrm{axis}$ at $B$. $P\left(4, -1\right)$ divides $AB$ in the ratio $1:2$.

Find the coordinates of $A \mathrm{and} B$.

The equation of a line ${\alpha }_1$ is $y=-8$ 

Write the slope of the line ${\alpha }_2$ if ${\alpha }_2$, is the bisector of $\angle O$.

The side $AB$ of a square $ABCD$ is parallel to the Y-axis as shown in the given figure.

Calculate the slope of $AC.$ [Given,$\tan (90+\theta )=-cot\theta$] 

The side $\mathrm{AB}$ of a square $\mathrm{ABCD}$ is parallel to the $\mathrm{Y}-$axis as shown in the given figure.

Calculate the slope of $\mathrm{BD}$.

The side $\mathrm{AB}$ of a square $\mathrm{ABCD}$ is parallel to the $\mathrm{Y}-$axis as shown in the given figure.

Calculate the slope of $\mathrm{AD}$.

Find the value of $a$, if the lines $\frac{y}{2}=x-p \text{and} ax+5=3y$ are parallel to each other.

Find the value of $p$, if the lines $y=3x+7$ and $y+px=3$ are parallel to each other.

Given two straight lines $kx-2y=5$ and $2x+3y+7=0$. If the given pair of lines is perpendicular, then find the value of $k$.

If the points $\left(2,-5\right)$, $\left(p-1,p+4\right)$ and $\left(4,3\right)$ are collinear, then the value of $p$.

The line passing through $A (- 2, 3)$ and $B (4, b)$ is perpendicular to the line $2x-4y=5$. Find the value of $b$.

The equation of a line is $3\mathrm{x}+4\mathrm{y}-7=0$. Find the slope of the line.

Find the equation of the line through the point $A\left(0,-3\right)$ and parallel to the line joining the points $M\left(3,2\right)$ and $N\left(-1,0\right)$.

 In the given figure, a straight line passes through the points $P\left(-1,4\right)$ and $Q\left(5,-2\right)$. It intersects the coordinate axes at points$A$ and $B$. If $M$ is the midpoint of the segment $AB$, then find the coordinates of $A$ and $B$.

 In the given figure, a straight line passes through the points $P\left(-1,4\right)$ and $Q\left(5,-2\right)$. It intersects the coordinate axes at points $A$ and $B$. If $M$ is the midpoint of the segment $AB,$ then find the equation of the line.