Write a system of inequalities to represent the shaded portion of the graph. Look at picture for the graph. Will Mark Brainliest.

The system of inequalities that represents the shaded portion is

y ≤ -x + 4

y > x

Step-by-step explanation:

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

The rule of the slope is m = , where

Let us find the equation of each line using the given figure

1. The solid line

∵ Points (4, 0) and (0, 4) lie on the solid line

∴ x1 = 4 and y1 = 0

∴ x2 = 0 and y2 = 4

→ Substitute them in the rule of the slope to find it

∵ m =

∴ m = -1

∵ The line intersects the y-axis at point (0, 4)

∴ b = 4

∵ The line is solid and the shading is under the line

∴ The sign of inequality is ≤

∴ The inequality is y ≤ -x + 4

2. The dashed line

∵ Points (0, 0) and (3, 1) lie on the dashed line

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 1

→ Substitute them in the rule of the slope to find it

∵ m =

∴ m =

∵ The line intersects the y-axis at point (0, 0)

∴ b = 0

∵ The line is dashed and the shading is over the line

∴ The sign of inequality is >

∴ The inequality is y > x + 0

∴ The inequality is y > x

The system of inequalities that represents the shaded portion is

y ≤ -x + 4

y > x