Question

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

Answer 1

Answer:

Step-by-step 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

$2x-4>y\to y$

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

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

$2x-y$        add y to both sides

$2x$           add 2 to both sides

$2x+22x+2$

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

$y$

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