The graph of a system of inequalities is shown.

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?

y > 2x
x + 2y ≤ –8
y ≥ 2x
x + 2y < –8
y < 2x
x + 2y ≥ –8
y ≤ 2x
x + 2y > –8

Question

06-01-2020
Mathematics

contestada

The graph of a system of inequalities is shown.

On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 6, negative 1) and (0, negative 4). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 2, negative 4) and (0, 0). Everything to the left of the line is shaded.
Which system is represented by the graph?

y > 2x
x + 2y ≤ –8
y ≥ 2x
x + 2y < –8
y < 2x
x + 2y ≥ –8
y ≤ 2x
x + 2y > –8

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calculista calculista · Answer 1 · 2020-01-13T15:11:23+01:00

Answer:

The system is

[tex]x+2y \leq -8[/tex]

[tex]y> 2x[/tex]

Step-by-step explanation:

Part 1

Find the equation of the first inequality

we know that

The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)

The slope is equal to

[tex]m=(-4+1)/(0+6)\\m=-0.5[/tex]

The equation of the solid line in slope intercept form is

[tex]y=-0.5x-4[/tex]

Everything below the line is shaded

so

The inequality is

[tex]y \leq -0.5x-4[/tex]

Convert to standard form

Adds 0.5x both sides

[tex]0.5x+y \leq -4[/tex]

Multiply by 2 both sides

[tex]x+2y \leq -8[/tex] -----> First inequality

Part 2

Find the equation of the second inequality

we know that

The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)

This line represent a proportional relationship, because the line passes through the origin

The slope is equal to the constant of proportionality

[tex]k=(-4)/(-2)=2[/tex]

The equation of the dashed line is

[tex]y=2x[/tex]

Everything to the left of the line is shade

so

The inequality is

[tex]y> 2x[/tex] -----> Second inequality

see the attached figure to better understand the problem

lexisixela lexisixela · Answer 2 · 2020-02-24T18:01:02+01:00

lexisixela lexisixela

24-02-2020

Answer:

the correct anwser is A.......

y > 2x

x + 2y ≤ –8 just took the unit test

Step-by-step explanation:

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