Answer: From graph,
inequality 1: y > [tex]\frac{2}{3}[/tex]x+(-2)
inequality 2: y > (-4)x+2
Step-by-step explanation:
The graph shows two lines on the X-Y plane.
Step 1: Find the equation of a line.
From figure, One line is passing through (3,0) and (0,-2)
Slope of line is given by m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{(-2)-0}{0-3}[/tex]
m=[tex]\frac{2}{3}[/tex]
Y-intercept isc=(-2)
The equation of line is given by y=mx+c
Therefore, y=[tex]\frac{2}{3}[/tex]x+(-2)
From figure, Another line is passing through (0.5,0) and (0,2)
Slope of line is given by m=[tex]\frac{Y2-Y1}{X2-X1}[/tex]
m=[tex]\frac{2-0}{0-0.5}[/tex]
m=[tex]\frac{2}{-0.5}[/tex]
m=(-4)
Y-intercept isc=(2)
The equation of line is given by y=mx+c
Therefore, y=(-4)x+2
Step 2: Test of origin and finding inequality
For y=[tex]\frac{2}{3}[/tex]x+(-2)
Let suppose, y > [tex]\frac{2}{3}[/tex]x+(-2)
This line is shaded toward the origin then, inequality must satisfy the origin
Test for origin says,
0 > [tex]\frac{2}{3}[/tex](0)+(-2)
0 > (-2)
TRUE.
y > [tex]\frac{2}{3}[/tex]x+(-2) is required inequality
For y=(-4)x+2
Let suppose, y > (-4)x+2
This line is shaded away from the origin then, inequality must not satisfy the origin
Test for origin says,
0 > [tex]\frac{2}{3}[/tex](0)+(-2)
0 > (+2)
FALSE, so that y > (-4)x+2 does not satisfy the origin
y > (-4)x+2 is required inequality
Thus,
inequality 1: y > [tex]\frac{2}{3}[/tex]x+(-2)
inequality 2: y > (-4)x+2
