Question

Solve the inequalities by graphing. Select the correct graph. 2x - y > 4 2x - y < -2

Answer 1

The graph is attached below.

However, just for an explanation; its middle section is white, purple to the left, teal to the right.

Explanation:

Answer 2

Explanation:

The slope form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

We only need two points to draw a line.

Convert to the slope-intercept form.

`2x-y>4` add y to both sides

`2x>y+4` subtract 4 from both sides

`2x-4>y\to y<2x-4`

Choice two values of x, put to the equation y = 2x - 4:

for x = 0

`y=2(0)-4=0-4=-4\to(0,\ -4)`

for x = 2

`y=2(2)-4=4-4=0\to(2,\ 0)`

`2x-y<-2` add y to both sides

`2x<y-2` add 2 to both sides

`2x+2<y\to y>2x+2`

y = 2x + 2

for x = 0

`y=2(0)+2=0+2=2\to(0,\ 2)`

for x = 2

`y=2(2)+2=4+2=6\to(2,\ 6)`

<, > - dotted line

≤, ≥ - solid line

<, ≤ - we shade the region below the line

>, ≥ - we shade the region above the line

`y<2x-4`

dotted line passes through (0, -4) and (2, 0), we shade the region below the line

`y>2x+2`

dotted line passes through (0, 2) and (2, 6), we shade the region above the line