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

y < 2/3 x - 1 is the linear inequality which represented by the graph ⇒ 4th answer

Step-by-step explanation:

* Lets explain how to solve the problem

- At first lets find the equation of the line

∵ The line passes through points (3 , 1) and (-3 , -3)

∵ The form of the equation is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The rule of the slope of any line passes through points (x1 , y1) and

  (x2 , y2) is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the intersection between the line and the

  y-axis at point (0 , c)

∵ (3 , 1) and (-3 , -3) are two points on the line

- Let (x1 , y1) is (3 , 1) and (x2 , y2) is (-3 , -3)

∴ The slope of the line m = (-3 - 1)/(-3 - 3) = -4/-6 = 2/3

∵ The line intersects the y-axis at point (0 , -1)

∴ c = -1

∵ The equation of the line is y = mx + c

∴ The equation of the line is y = 2/3 x + -1

∴ The equation of the line is y = 2/3 x - 1

- If the shaded part is over the line then the sign of inequality is ≥ or >

- If the shaded part is under the line then the sign of inequality is ≤ or <

- If the line represented by solid line (not dashed), then the sign of

 inequality is ≥ or ≤

- If the line represented by dashed line (not solid), then the sign of

 inequality is > or <

∵ The shading part is under the line

∵ The line is dashed

∴ The sign of the inequality is <

∴ y < 2/3 x - 1

* y < 2/3 x - 1 is the linear inequality which represented by the graph

7

step-by-step explanation: