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., $y\geq \frac{3}{2} x+\frac{1}{5}$.

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,

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

$y-0.2=\frac{2.2-0.2}{3-0}(x-0)$

$y-\frac{1}{5} =\frac{2}{3} x$

$y =\frac{2}{3} x+\frac{1}{5}$

The equation of the line is $y =\frac{2}{3} x+\frac{1}{5}$.

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.

$(0)=\frac{2}{3} (1)+\frac{1}{5}$

$(0)=\frac{2}{3} +\frac{1}{5}$

$(0)=\frac{10+3}{15}$

$(0)=\frac{13}{15}$

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

$y \leq \frac{2}{3} x+\frac{1}{5}$

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