Question

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

Answer 1

y ≤ -5/3x + 11/3

Explanation:

line pass : (1,2) (4,-3)

slope (m) = (-3 - 2) / (4 - 1) = - 5/3

equation: (y-2) / (x-1) = -5/3 y-2 = -5/3x + 5/3

y = -5/3x + 11/3

(-2,8) : not solution y ≤ -5/3x + 11/3

Answer 2

y < -x + 4

y < x + 4

Explanation:

To answer this problem, it is easiest to first plot the three points.

Then draw two lines that intersect below point (-2, 8) on the y-axis.

Then find the equations of the two lines, and write two inequalities based on the lines that intersect below the lines.

y < -x + 4

y < x + 4