Answer :

Ashraf82

Answer:

The inequality represented by the graph is y >  [tex]\frac{1}{2}[/tex] x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept (value y at x = 0)

The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where

  • (x1, y1) and (x2, y2) are two points on the line

From the given figure

∵ The line passes through points (0, 2) and (2, 3)

∴ x1 = 0 and y1 = 2

∴ x2 = 2 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = [tex]\frac{3-2}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

m =  [tex]\frac{1}{2}[/tex]

→ b is the value of y at x = 0

∵ At x = 0, y =2

b = 2

→ Substitute the value of m and b in the form of the equation above

∵ y =  [tex]\frac{1}{2}[/tex] x + 2

The equation of the line is y =  [tex]\frac{1}{2}[/tex] x + 2

∵ The line is dashed

∵ The shaded area is over the line

The sign of inequality is >

→ Replace = in the equation by >

y >  [tex]\frac{1}{2}[/tex] x + 2

The inequality represented by the graph is y >  [tex]\frac{1}{2}[/tex] x + 2

Other Questions