Question : What is the equation of the line perpendicular to the line $2x+3y=-6$ and having y-intercept 3?

Option 1: $3x-2y=6$

Option 2: $3x-2y=-6$

Option 3: $2x-3y=-6$

Option 4: $2x-3y=6$

Question : The area of the triangle formed by the graph of the straight lines $x-y=0$, $x+y=2$, and the $x$-axis is:

Option 1: 1 sq. unit

Option 2: 2 sq. units

Option 3: 4 sq. units

Option 4: 5 sq. units

Question : The graph of $3x+4y-24=0$ forms a $\triangle OAB$ with the coordinate axes, where $O$ is the origin. Also, the graph of $x+y+4=0$ forms a $\triangle OCD$ with the coordinate axes. Then the area of $\triangle OCD$ is equal to:

Option 1: $\frac{1}{2}\text{ of the area of}\ \triangle OAB$

Option 2: $\frac{1}{3}\text{ of the area of}\ \triangle OAB$

Option 3: $\frac{2}{3}\text{ of the area of}\ \triangle OAB$

Option 4: $\text{ the area of}\ \triangle OAB$

Question : What is the area (in sq. units) of the triangle formed by the graphs of the equations $2x + 5y - 12=0, x + y = 3,$ and $y = 0$?

Option 1: 3

Option 2: 2

Option 3: 5

Option 4: 6

Question : The area of triangle with vertices A(0, 8), O(0, 0), and B(5, 0) is:

Option 1: 8 sq. units

Option 2: 13 sq. units

Option 3: 20 sq. units

Option 4: 40 sq. units