Answer:
Step-by-step explanation:
The slope form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We only need two points to draw a line.
Convert to the slope-intercept form.
[tex]2x-y>4[/tex] add y to both sides
[tex]2x>y+4[/tex] subtract 4 from both sides
[tex]2x-4>y\to y<2x-4[/tex]
Choice two values of x, put to the equation y = 2x - 4:
for x = 0
[tex]y=2(0)-4=0-4=-4\to(0,\ -4)[/tex]
for x = 2
[tex]y=2(2)-4=4-4=0\to(2,\ 0)[/tex]
[tex]2x-y<-2[/tex] add y to both sides
[tex]2x<y-2[/tex] add 2 to both sides
[tex]2x+2<y\to y>2x+2[/tex]
y = 2x + 2
for x = 0
[tex]y=2(0)+2=0+2=2\to(0,\ 2)[/tex]
for x = 2
[tex]y=2(2)+2=4+2=6\to(2,\ 6)[/tex]
<, > - dotted line
≤, ≥ - solid line
<, ≤ - we shade the region below the line
>, ≥ - we shade the region above the line
[tex]y<2x-4[/tex]
dotted line passes through (0, -4) and (2, 0), we shade the region below the line
[tex]y>2x+2[/tex]
dotted line passes through (0, 2) and (2, 6), we shade the region above the line
