The linear inequality depicted by the graph is: [tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:
[tex]m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}[/tex]
Hence the equation of the line is:
[tex]y = \frac{2}{3}x + 0.2[/tex]
[tex]y = \frac{2}{3}x + \frac{1}{5}[/tex]
The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:
[tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]
More can be learned about linear equations at https://brainly.com/question/24808124
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