The true statements are:
The area below the line is shaded ⇒ 3rd
The x-intercept of the boundary line is (Negative three-halves, 0) ⇒ 5th
Step-by-step explanation:
In the graph of inequalities
- If the sign of inequality is ≤ or ≥, then it represented by a solid line
- If the sign of inequality is < or >, then it represented by dashed line
- The solutions of inequality y < .... is in the shaded area under the line
- The solutions of inequality y > .... is in the shaded area over the line
∵ The inequality is y < [tex]\frac{2}{3}[/tex] x + 1
∵ The form of the inequality is y < mx + b, where m is the
  slope of the line and b is the y-intercept
∴ The slope of the line is [tex]\frac{2}{3}[/tex]
∴ The slope of the line is not 1
∵ y < [tex]\frac{2}{3}[/tex] x + 1
- The line which represents the inequality is not solid because
 the sign of inequality is < not ≤
∴ The line is not solid
∵ y < [tex]\frac{2}{3}[/tex] x + 1
- The area below the line is shaded because the sign of
  inequality is <
∴ The area below the line is shaded
∵ y < [tex]\frac{2}{3}[/tex] x + 1
∵ x = 2 and y = 3
- Substitute x and y in the inequality by 2 and 3, if the inequality
 is right then (2 , 3) is a solution to the inequality
∵ 3 < [tex]\frac{2}{3}[/tex] (2) + 1
∴ 3 < [tex]\frac{4}{3}[/tex] + 1
∴ 3 < [tex]\frac{7}{3}[/tex]
- 3 is not smaller than [tex]\frac{7}{3}[/tex]
∴ (2 , 3) is not a solution to the inequality
∵ y < [tex]\frac{2}{3}[/tex] x + 1
∵ x-intercept means value x if y = 0
- Substitute y by 0 and equate it by the right hand side of the inequality
∵ 0 = [tex]\frac{2}{3}[/tex] + 1
- Subtract 1 from both sides
∴ -1 = [tex]\frac{2}{3}[/tex] x
- Divide both sides by [tex]\frac{2}{3}[/tex]
∴ [tex]\frac{-3}{2}[/tex] = x
∴ The x-intercept of the boundary line is ( [tex]\frac{-3}{2}[/tex] , 0)
The true statements are:
The area below the line is shaded
The x-intercept of the boundary line is (Negative three-halves, 0)
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