The linear inequality represented by the given graph in the attached image is y > -3x + 6.
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The graph of the linear inequality. Let's pick two points from the graph to frame the linear equation
The slope-intercept form of the equation is Where m is the slope and b is the y-intercept is (0,6) from the graph so b=6.
Find out slope m by using the general formula. Pick two points (0,6) and (2,0).
Slope = ( y₂ - y₁) / ( x₂ - x₁ )
Slope = ( 0 - 6 ) / ( 2 - 6 )
Slope = -3
m = -3
So the equation is y = -3x + 6
Now we check the inequality sign by testing any point on the shaded area let's pick (4,0). let's plug in 4 for x and 0 for y
y= -3x + 6
0 = -3(4) + 6
0 > -6
Inequality: y > -3x + 6.
Therefore, the inequality represented by the given graph is y > -3x + 6.
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