M L Aggarwal Solutions for Exercise 2: Exercise 12.2

The straight lines $y=3x-5$ and $2y=4x+7$ are parallel.

If $6x+5y-7=0$ and $2px+5y+1=0$ are parallel lines, find the value of $p$.

If the straight lines $3x-5y+7=0$ and $4x+ay+9=0$ are perpendicular to one another, find the value of $a$.

If the lines $3x+by+5=0$ and $ax-5y+7=0$ are perpendicular to each other, find the relation connecting $a$ and $b$.

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 $b$.

Find the equation of the line that is parallel to $2x+5y-7=0$ and passes through the mid-point of the line segment joining the points $\left(2, 7\right)$ and $\left(-4, 1\right)$.

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

The points $B\left(1, 3\right)$ and $D\left(6, 8\right)$ are two opposite vertices of a square $ABCD$. Find the equation of the diagonal $AC$.