Question

Which of the following is the correct solution to the linear inequalities shown below

Answer 1

The inequality function is given .

`y\leq(2)/(3)x+1`

To draw the graph of the inequality function , first determine the coordinates of the function.

At x equal to 0.

`y=(2)/(3)(0)+1`
`y=1`

At y equal to 0.

`0=(2)/(3)x+1`
`-(2)/(3)x=1`
`x=(-3)/(2)`
`x=-1.5`

The coordinates at which the function satisfy are obtained as,

`(0,1),(-1.5,0)`

For the inequality of the function given is less than equal to that means the shaded region of the graph lies below the origin .

Therefore the garph of the inequality of the function is,

According to the options given A,B,C and D.

The correct option is A.

Reason : The ineqaulity graph is always represented by dashed line.