1.
The line joins (0, -2) and (1, 3).
thus, the slope of this line is
[tex] \frac{y_1-y_2}{x_1-x_2}= \frac{-2-3}{0-1}= \frac{-5}{-1}=5 [/tex]
Using point (0, -2) and slope m=5, the equation of the line is:
y-(-2)=5(x-0)
y+2=5x
5x-y=2
2.
Thus the candidate inequalities are
5x-y≥2 and 5x-y≤2
3.
Pick a point P not on the line, for example P(0, -3) which is clearly below the line, which is the shaded part.
check (x,y)=(0,-3) in 5x-y≥2:
5*0-(-3)≥2
3≥2, which is true
Remark: If we had picked a point above the line, for example P(0,2), we would have
5x-y≥2:
5*0-2≥2:
-2≥2, not true, but we would pick again this inequality, since the second point was not on the colored region.
Answer:
5x-y≥2
