Write a system of linear inequalities so the points (1, 2) and (4, -3) are solutions of the system, but the point (-2, 8) is not a solution of the system.

Step-by-step explanation:

(1, 2) and (4, -3)

First, find the slope (m):

m =

   =

Next, choose ONE of the points and input the point and slope into the Point-Slope formula: y - y₁ = m(x - x₁)

y - 2 = (x - 1)

y - 2 = +

y      = +

Then, determine which inequality symbol will result in (-2, 8) being False (since it is not a solution):

y ___ +

8 ___ +

8 ___

8 >

so ≤ makes the statement False

⇒ y ≤ +

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If you need a "system" of inequalities, then you need another equation.

There are infinite possibilities. Graph the points to see what works.  

y < 8   or  x > -2 are two examples.

---> I just realized that the system can be simpler than what I did above: