Question

Graph question

Answer 1

anyone

Answer 2

They put my in algebra 1 instead of prealgebra so im kind of suffering

Answer 3

@pitamar

Answer 4

@bCXvsfdgsdfgd999

Answer 5

Sorry, I'm back now.
Well first it writes 'HELL' on top of the image lol

Well here is a walk through:

Let's see. In order to solve this kind of problems we have to basically examine the equation of the edge. The straight line in our case.
So let's ignore the 'blue' area above it for now, and just try to find the equation for the line.

To do so we have to recognize two points we can easily tell the line passes through and then we can form a line equation using them.
For example, let's pick point A at (3,1) because it's clear from the graph that the line passes there, and B at (-1, -5). Notice I tried to pick points where the coordinates are clear to see by the drawn grid.

Now let's examine how the line behaves between those points.
We can tell that
$$
\text{x_difference} = \Delta x = A_x - B_x = 3 - (-1) = 4 \\
\text{y_difference} = \Delta y = A_y - B_y = 1 - (-5) = 6
$$It means that the 'y' value on the line has raised by 6 for an addition of 4 to the 'x'.
Because this is a line, we can tell its rate of change is constant. This rate of change is the 'slope' of the line and basically describe the ratio of how much 'y' changes for a change in the 'x':
$$
\text{slope} = m = \frac{\Delta y}{\Delta x} = \frac{6}{4} = \frac{3 \cdot \cancel 2}{2 \cdot \cancel 2} = \frac{3}{2}
$$This means, that every 2 added to the 'x' causes 3 added to the 'y':
$$ m \cdot 2 = \frac{3}{2} \cdot 2 = 3$$
6 added to the 'x' will cause an addition of 9 to the 'y':
$$
m \cdot 6 = \frac{3}{2} \cdot 6 = \frac{3}{2} \cdot (2 \cdot 3) = 3\cdot 3 = 9
$$
That leads us to an initial equation:
$$
y = m \cdot x \\
y = \frac{3}{2} \cdot x
$$Which matches the above inspected behavior because if you notice, every 1 added to 'x' causes an addition of another \(\frac{3}{2}\) to the value of 'y'.
However this is not enough, because we only described how our line behaves for a change in 'x'. The value of 'y' could however be determined also by something not related to the change of 'x', a constant. So our equation becomes:
$$
y = m \cdot x + c \\
y = \frac{3}{2}\cdot x + c
$$Notice that no matter what 'c' is, adding 1 to 'x' will still add \(\frac{3}{2}\) to 'y'.
In order to find what that constant is we have to take a point the line passes through and plug it into the equation and see what constant would make it true.
Let's try our point A:
$$
y = A_y = 1 \qquad x = A_x = 3\\
1 = \frac{3}{2} \cdot 3 + c \\
c = 1 - \frac{9}{2} = \frac{2 - 9}{2} = -\frac{7}{2} = -3.5
$$ At last, we have the line's equation:
$$
y = \frac{3}{2} \cdot x - 3.5
$$Notice it matches the line in the graph. for example at x=0 we have y = -3.5.
Now, we have a solid line with painted area above it. that means that for any 'x', the 'y' could be equal or greater than the 'y' value of the line.
If it could only be 'greater' but not equal, then the line would have been dashsed instead.
Look here for examples:
http://www.mathsisfun.com/algebra/graphing-linear-inequalities.html

So now we can say:
$$
y \ge \frac{3}{2} \cdot x - 3.5
$$And we can form it a little bit more like they do in the answers:
$$
2 \cdot (y) \ge 2 \cdot \Big( \frac{3}{2} \cdot x - 3.5 \Big) \\
2y \ge 3x - 7 \\
\cancel{2y} + (7 - \cancel {2y}) \ge 3x - \cancel 7 + ( \cancel 7 - 2y) \\
7 \ge 3x - 2y \\
3x - 2y \le 7
$$Hope it's clear =)