Answer:
![y](https://tex.z-dn.net/?f=y%3C-%5Cdfrac%7B1%7D%7B4%7D%20x%2B1%5C%5COR%5C%5C%204y%3C-x%2B4)
Step-by-step explanation:
First of all, let us try to find out the equation.
We can easily observe from the graph the values of x and y intercept.
x intercept is the value where y coordinate is 0.
We can see that y is 0 at x = 4
So, x intercept (4, 0)
y intercept is the value where x coordinate is 0.
We can see that y is 1 at x = 0
So, x intercept (0, 1)
Now, we have 2 points for the equation of line.
Slope intercept form:
![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
Slope of a line:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![x_1 = 0\\x_2 = 4\\y_1 = 1\\y_2 = 0](https://tex.z-dn.net/?f=x_1%20%3D%200%5C%5Cx_2%20%3D%204%5C%5Cy_1%20%3D%201%5C%5Cy_2%20%3D%200)
![m=\dfrac{0-1}{4-0}\\\Rightarrow m =-\dfrac{1}{4 }](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B0-1%7D%7B4-0%7D%5C%5C%5CRightarrow%20m%20%20%3D-%5Cdfrac%7B1%7D%7B4%20%7D)
![y=-\dfrac{1}{4} x+c](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B1%7D%7B4%7D%20x%2Bc)
Putting the point (0, 1):
![1=-\dfrac{1}{4} \times 0+c\\\Rightarrow c = 0](https://tex.z-dn.net/?f=1%3D-%5Cdfrac%7B1%7D%7B4%7D%20%5Ctimes%200%2Bc%5C%5C%5CRightarrow%20c%20%3D%200)
So, the equation becomes:
![y=-\dfrac{1}{4} x+1](https://tex.z-dn.net/?f=y%3D-%5Cdfrac%7B1%7D%7B4%7D%20x%2B1)
Let us try to put a point (0, 0) in the equation.
LHS becomes 0.
RHS becomes 1.
LHS < RHS (Only less than sign used because the line is dashed not solid)
So, the inequality is:
![y](https://tex.z-dn.net/?f=y%3C-%5Cdfrac%7B1%7D%7B4%7D%20x%2B1%5C%5COR%5C%5C%204y%3C-x%2B4)