Question

Can I get some help

Answer 1

Select the inequality that corresponds to the given graph.

graph of an inequality with a dashed line through the points negative 3 comma 0 and 0 comma 4 and shading below the line

4x − 3y > − 12
x + 4y > 4
4x − 2y < − 8
2x + 4y ≥ − 16

Answer 2

Inequalities always detemine a certain region of points that satisfies the conditions given.
I would suggest you find the equation of the line tha limits the solution plane with the "empty" set of points.

With that I mean, find the line that divides the shaded region, with the non-shaded one.

Answer 3

I have no idea how to solve it. Is there a formula I should follow or a set of steps @Owlcoffee

Answer 4

Well, a formula that strictly can give you the solution... no.
But there are a series of steps yes, these being:
(1) find the equation of the dividing line
(2) leave the variables on one side of the inequality
(3) plot one point of the plane in the equation and draw the solution region.

Answer 5

How do I do that? @Owlcoffee

Answer 6

Let's begin by finding the equation of the line that divides the planes:
You can see the line has two notable points, these being the root \(M(-3,0)\) and the y-intersection \(P(0,4)\), these two points are enough to determine the equation of the line.
First off, find the slope with the formula: \(m=\frac{ y_2-y_1 }{ x_2-x_1 }\)
\[m=\frac{ 4-0 }{ 0+3 }\]

Answer 7

so 4/3? @Owlcoffee

Answer 8

Yes, now, using one of the points and the value of that slope you can use the form:
\[(y-y_o)=m(x-x_o)\]
let's say we use point P:
\[(y-4)=(\frac{ 4 }{ 3 })(x-0)\]

Answer 9

What are the values for x and y @Owlcoffee

Answer 10

They don't matter for now.
What they represent are the pattern all the coordinates composing the line follow.
Have you simplified that yet?

Answer 11

Sorry I'm not too sure how to work it out. Can you show me how to do it? @Owlcoffee

Answer 12

\[(y-4)=\frac{ 4 }{ 3 }(x)\]
\[\frac{ 4 }{ 3 }x-y+4=0 \]
\[4x-3y+12=0\]
And that final one is the equation of the line that divides the solution plane with the "empty" one.