Find a linear inequality with the following solution set. Each grid line represents one unit.

(Give your answer in "standard form"  ax + by + c > 0 or ax + by + c >= 0 where a b and c are integers with no common factor other than 1.)

 Nov 28, 2023

To find a linear inequality with the given solution set, we need to consider the shaded region. Let's denote the coordinates of the shaded region's vertices.


Looking at the image, we can see that the shaded region is below and to the left of the line passing through the points (4, 1) and (5, 3). We can use these two points to find the equation of the line in slope-intercept form (y = mx + b):

First, find the slope (m): m=5−43−1​=2


Now, we can use the slope and one of the points (let's use (4, 1)) to find the y-intercept (b): 2⋅47b=−7

So, the equation of the line is y=2x−7.


Now, since we want the shaded region to be below and to the left of this line, we want the region where y<2x−7.


We can rewrite this inequality in standard form (ax + by + c > 0) by moving all terms to one side



So, the linear inequality that represents the shaded region in standard form is −2x+y+7<0.

 Nov 29, 2023

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