The inequality that represents the graph in the given diagram is: y ≥ 4x - 6.
How to Write the Inequality that Represents a Graph?
The inequality sign to use depends on the boundary line, whether it is dashed or solid line. And also, it depends on where the shaded area of the graph lies, above or below the boundary line.
The boundary line in the graph is a solid line, and the shaded area is above the boundary line, therefore, the inequality sign we would use is, "≥".
Find the slope (m) of the boundary line.
Slope (m) = rise/run = 4 units / 1 unit
Slope (m) = 4
The y-intercept (b) is -6 [this is where the value of x = 0, and also the point where the y-axis is intercepted].
Substitute m = 4 and b = -6 into y ≥ mx + b
y ≥ (4)x + (-6)
y ≥ 4x - 6
Thus, the inequality that represents the graph in the given diagram is: y ≥ 4x - 6.
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