On a coordinate plane, 2 straight lines are shown. the first solid line has a positive slope and goes through (0, negative 2) and (2, 0). everything to the left of the line is shaded. the second dashed line has a negative slope and goes through (0, 2) and (4, 0). everything below and to the left of the line is shaded. which system of linear inequalities is represented by the graph? y > x – 2 and x – 2y < 4 y > x + 2 and x + 2y < 4 y > x – 2 and x + 2y < 4 y > x – 2 and x + 2y < –4

Step-by-step explanation:

step 1

Find the equation of the first inequality

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

Find the slope

The formula to calculate the slope between two points is equal to

substitute the values

The equation in slope intercept form is equal to

we have

---> the y-intercept is given

substitute

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

step 2

Find the equation of the second inequality

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

Find the slope

The formula to calculate the slope between two points is equal to

substitute the values

The equation in slope intercept form is equal to

we have

---> the y-intercept is given

substitute

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

Rewrite

Multiply by 2 both sides

therefore

The system of inequalities is

see the attached figure to better understand the problem

linear pair postulates