Answer:
The inequality shown in the graphic is ![y > 4x + 1](https://tex.z-dn.net/?f=y%20%3E%204x%20%2B%201)
Step-by-step explanation:
Equation of a line:
The equation of a line is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which m is the slope and b is the y-intercept(value of y when x = 0).
Inequality:
Values greater than the dashed line, dashed so the line is not part of the inequality, thus, the inequality is:
![y > mx + b](https://tex.z-dn.net/?f=y%20%3E%20mx%20%2B%20b)
Dashed line:
The dashed line goes through (0,1) and (1,5).
Point (0,1) means that when
, so
, and:
![y > mx + 1](https://tex.z-dn.net/?f=y%20%3E%20mx%20%2B%201)
Finding the slope:
When we have two points, the slope is given by the change in y divided by the change in x. In this question, we have point (0,1) and (1,5), so:
Change in y: 5 - 1 = 4
Change in x: 1 - 0 = 1
Slope: ![m = \frac{4}{1} = 4](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B4%7D%7B1%7D%20%3D%204)
What inequality is shown in the graph?
![y > 4x + 1](https://tex.z-dn.net/?f=y%20%3E%204x%20%2B%201)