Question

Which linear inequality is represented by the graph? y > 2/3x – 1/5 y ≥ 3/2x + 1/5 y ≤ 2/3x + 1/5 y < 3/2x – 1/5

Answer 1

Answer: The correct option is third, i.e.,
`y\geq (3)/(2) x+(1)/(5)`.

Step-by-step explanation:

From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).

The equation of line passing through two points is,

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)`

`y-0.2=(2.2-0.2)/(3-0)(x-0)`

`y-(1)/(5) =(2)/(3) x`

`y =(2)/(3) x+(1)/(5)`

The equation of the line is
`y =(2)/(3) x+(1)/(5)`.

From the figure it is noticed that as the value of x increases the value of y is less.

he point (1,0) lies on the shaded reason it means this point must satisfy the equation.

`(0)=(2)/(3) (1)+(1)/(5)`

`(0)=(2)/(3) +(1)/(5)`

`(0)=(10+3)/(15)`

`(0)=(13)/(15)`

It is true of the sign is less than or equal to instead of equal.

`y \leq (2)/(3) x+(1)/(5)`

Therefore, option third is correct.

Answer 2

What you must do for this case first is to find the equation of the line.
We have then that by substituting the values of x = 0 and x = 3 we obtain:
y = 0.2
y = 2.2
Respectively.
So, the line is:
y = 2 / 3x + 1/5
Then, the points that satisfy the inequality are all those of the shaded region.
Answer:
The inequality is:
y ≤ 2 / 3x + 1/5