Question

50 POINTS FOR CORRECT AWNSER!

Answer 1

Answer: y > x + 4

Explanation:

First lets find a linear equation for the dividing line, in the form:

y = mx + b

We know that b is 4, since this is the y-intercept

lets use any point on the graph, I'll use (-4, 0):

y = mx + 4

0 = m(-4) + 4

-4 = -4m

m = 1

So the slope is 1. Our completed formula for the line is:

y = x + 4

Since the left side of this graph is shaded, we know it will either be > or ≥. Since the line is also dotted we know it is denoted by a simple ">" sign.

So our completed inequality equation is: y > x + 4

Hope this helped!

Answer 2

`\sf y > x+4`

Explanation:

Choose 2 points on the line: (-4, 0) and (0, 4)

• Let
  `\sf (x_1,y_1)=(-4,0)`
• Let
  `\sf (x_2,y_2)=(0,4)`

`\sf slope=(y_2-y_1)/(x_2-x_1)=(4-0)/(0-(-4))=1`

point-slope form of linear equation:
`\sf y-y_1=m(x-x_1)`

`\implies \sf y-0=1(x-(-4))`

`\implies \sf y=x+4`

Solid line : ≤ or ≥

Dashed line: < or >

Therefore as the line is dashed, and the shading is above the line,

`\implies \sf y > x+4`