99.3k views
15 votes
PLEASE HURRY!! Find the inequality represented by the graph

PLEASE HURRY!! Find the inequality represented by the graph-example-1
User Mcruz
by
3.0k points

1 Answer

8 votes

Answer:

The inequality represented by the graph is y >
(1)/(2) x + 2

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 =
(y2-y1)/(x2-x1) , 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 =
(3-2)/(2-0) =
(1)/(2)

m =
(1)/(2)

→ 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 =
(1)/(2) x + 2

The equation of the line is y =
(1)/(2) x + 2

∵ The line is dashed

∵ The shaded area is over the line

The sign of inequality is >

→ Replace = in the equation by >

y >
(1)/(2) x + 2

The inequality represented by the graph is y >
(1)/(2) x + 2

User UiUx
by
3.5k points