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