Based on the calculations, the inequality represented by the given graph is y ≤ -3/2x - 2.
What is an inequality?
An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
- Less than or equal to (≤).
- Greater than or equal to (≥).
What is a graph?
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
Based on the graph given, we have an inequation of the form y ≤ f(x), and f(x) is a linear function with following points:
Points (x, y) = (0, -2) and (2, -5)
Next, we would determine the slope as follows:
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-5 - (-2))/(2 - 0)
Slope, m = -3/2.
Mathematically, the point-slope form of a straight line is given by:
y - y₁ = m(x - x₁)
Where:
Substituting the given parameters into the formula, we have;
y - (-2) = -3/2(x - 0)
y + 2 = -3/2x
y = -3/2x - 2
y ≤ -3/2x - 2.
Read more on slope here: https://brainly.com/question/17106134
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