Question

Please help me with math

Answer 1

By observing the graph we can note down the following things about the boundary line:

1. It has a positive slope.
2. It cuts the X-axis at $(5,0)$
3. It cuts the Y-axis at $(0,-x)$, where $|x|$ is some value less than 2 but greater than 1.

Let's look at the shaded region. The origin lies inside it.

Thus, the point $(0,0)$ satisfies the equation of the region.

Upon putting it in the options, we find that only two options: 2 and 4 satisfy the inequality $0<5$

Now find the Y-intercept of the boundary line:

Option 4) $0-2y=5$

$y=\frac{-5}{2}<-2$

Since it is smaller than -2, it is the wrong option.

Hence, correct option is $\boxed{x-3y<5}$