Answer:
The inequality that represents the graph must have the following form:
[tex]y > -4\cdot x + 6[/tex]
Step-by-step explanation:
First, we need to determine the equation of the line which represents the "lower" bound of the inequality:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, horizontal axis.
[tex]y[/tex] - Dependent variable, vertical axis.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
Given two distinct points of the line, we can solve for both slope and intercept: [tex](x_{1}, y_{1}) = (1, 2)[/tex], [tex](x_{2}, y_{2}) = (0, 6)[/tex]
[tex]m + b = 2[/tex] (2)
[tex]b = 6[/tex] (3)
The solution of the system is: [tex]m = -4[/tex], [tex]b = 6[/tex]
Then, the inequation must have the following form:
[tex]y > -4\cdot x + 6[/tex]
