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Since 3x - 4y = -123x−4y=−12 is linear, the easiest place to start is to draw the line for that equation by determining the x and y axii intercepts.
When y = 0y=0 then 3x - 4y = -123x−4y=−12 becomes 3x = -123x=−12 or x = -4x=−4
When x = 0x=0 then 3x - 4y = -123x−4y=−12 becomes -4y = -12−4y=−12 or y = 3y=3
We can now draw the line for the equation 3x - 4y = -123x−4y=−12 by drawing a straight line through the two points (-4,0)(−4,0) and (0,3)(0,3)
All that remains is to determine which side of that line is represented by 3x - 4y = -123x−4y=−12
Consider the point (x,y) = (0,0)(x,y)=(0,0) and apply it to the given expression
3x - 4y >= -123x−4y≥−12 giving 3(0) - 4(0) >= -123(0)−4(0)≥−12 or 0 >= -120≥−12
Since this is obviously true (x,y) = (0,0)(x,y)=(0,0) must be within the area described by 3x - 4y >= -123x−4y≥−12
The required graph is therefore the unshaded area in the diagram (plus the line for 3x - 4y = -123x−4y=−12).
