niyahbailey3
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Select the inequality that corresponds to the given graph. Graph with a y-intercept at 0 comma 1 and a second point at negative 4 comma 0. This is a dashed line with shading above the line.

A. 4x-3y>-12
B. -x+4y>4
C. 4x-2y<-8
D. 2x+4y>_-16

Respuesta :

MrGumby

The correct answer is B) -x + 4y > 4.

The easiest way to find a graph in standard form is by using the zeros rule. If you start by plugging in a 0 for x, you'll get the y-intercept.

-x + 4y > 4

0 + 4y > 4

y = 1

(0, 1) was the first point you wanted to graph. Next we'll do the same with putting in a 0 for y to get the x-intercept.

-x + 4y > 4

-x + 4(0) > 4

-x + 0 > 4

-x > 4

x > -4

(-4, 0) is the second point. Therefore, this must be the graph you are looking for.

MrRoyal

Inequalities are used to represent unequal expressions

The inequality of the graph is [tex]- x + 4y > 4[/tex]

The graph passes through points (0,1) and (-4,0).

Start by calculating the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{0 - 1}{-4 - 0}[/tex]

[tex]m = \frac{1}{4}[/tex]

The linear inequality is calculated using:

[tex]y - y_1 - m(x - x_1) > 0[/tex] ---- the greater than inequality sign is used because the line above is shaded.

So, we have:

[tex]y - 1 - \frac 14(x - 0) > 0[/tex]

Open bracket

[tex]y - 1 -\frac 14x > 0[/tex]

Multiply through by 4

[tex]4y - 4 - x > 0[/tex]

Add 4 to both sides

[tex]4y - x > 4[/tex]

Rewrite as:

[tex]- x + 4y > 4[/tex]

Hence, the inequality of the graph is [tex]- x + 4y > 4[/tex]

Read more about inequalities at:

https://brainly.com/question/18881247

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