Which linear inequality is represented by the graph?

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First find the equation of the graph by using any two points on the line:

I will use the points (0, 3)  and (1,1)

Gradient = (3-1)/(0-1)=  2/-1 = -2

Generally, the equation of a line is given by y = mx + c,  where m is the gradient and c is the y intercept, i.e the value of y when x is 0,

m = -2

c = 3

so the equation is y = -2x + 3

Now choose any point in the graph that satisfy the conditions and substitute in the equation,

i,e. in the shade region

For me I choose (-2, 1)

y = -2x + 3

-2 = -2(-2) +3

-2 = 4+3

-2 < 7

So the linear equality represented by the above graph is y < -2x + 3

Please let me know if you need any clarification. I'm always happy to answer your questions.

Znljrngure (69)
University of Virginia

Just the thing I needed, saved me a lot of time.