Question

Enter an inequality that represents the graph in the box.

Answer 1

Since y=-1 when x=0 and we can write the equation (we'll turn it into an inequality later) as y=mx-1 from y=mx+b by plugging (0,1) in. Next, y equals 2 when x=1, so we plug those in to get 2=m*1-1. Adding 1 to both sides, we get 3=m, making our equation y=3x-1 (since y and x stay variables). Lastly, we turn it into an inequality, It seems to be inclusive to the line, so it's either 
3x-1≤y or 3x-1≥y. Finding a random point in the inequality (4, 1), we plug it in to get 12-1=11, which is clearly larger than 1, so we get 3x-1≥y.

Answer 2

Here we want to write the inequality that is represented with the given graph.

The answer is: y ≤ 3x - 1

Let's start by analyzing the graph:

We can see that the boundary is a solid line, and the shaded region is bellow that line, then the inequality will be something like:

y ≤ a*x + b

Then the first thing we need to do is to find the equation of the line.

Remember that if a given line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as.

$a = \frac{y_2 - y_1}{x_2 - x_1}$

Looking at the graph we can see that the line passes through the points

(-1, -4) and (1, 2)

$a = \frac{2 - (-4)}{1 - (-1)} = 3$

Then we have the line y = 3*x + b

To find the value of b, remember that the line should pass through the point (1, 2), then we can replace x = 1 and y = 2 in the above equation:

2 = 3*1 + b

2 = 3 + b

2 - 3 = b = -1

Then the inequality represented is:

y ≤ 3x - 1

If you want to learn more, you can read:

https://brainly.com/question/15748955