Which is the correct inequality for the given graph?

x + 3y < -3

x + 3y > -3

x - 3y < -1

3x + y > -1

The correct inequality for the given graph is x + 3y < -3 ⇒ 1st answer

Step-by-step explanation:

* Lets study the graph

- The angle between the positive part of x-axis and the line is obtuse,

 that means the slope of the line is negative value

- The shaded part is under the line, that means the solutions of the

 inequality are under the line , so the sign of the inequality is <

- The y-intercept is < -1 ⇒ (the value of y when x = 0)

* Now lets check the answers to find the correct answer

- At first we will choose the answer with sign <

∴ The answers are x + 3y < -3 OR x - 3y < -1

- At second lets check the y-intercept (put x = 0)

- Substitute x by 0 in the two answer to choose the right one

∵ x = 0

∴ 0 + 3y < -3 ⇒ ÷ 3 both sides

∴ y < -1

* OR

∵ x = 0

∴ 0 - 3y < -1 ⇒ ÷ -3 both sides

∴ y > 1/3 ⇒ because we divide the inequality by negative number

  we must reverse the sign of inequality

∵ the y-intercept is < -1

∴The first equation is right

* To be sure check the slope of each line

∵ y < mx + c, where m is the slope of the line

- Put each inequality in this form

∵ x + 3y < -3 ⇒ subtract x from both sides

∴ 3y < -3 - x ⇒ ÷ 3

∴ y < -1 - x/3

∴ m = -1/3 ⇒ the slope is negative

* OR

∵ x - 3y < -1 ⇒ subtract x from both sides

∴ -3y < -1 - x ⇒ ÷ -3

∴ y > 1/3 + x/3

∴ m = 1/3 ⇒ the slope is positive

∵ The slope of the line is negative

∴ The correct inequality for the given graph is x + 3y < -3

the answer is a

step-by-step explanation: