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akjlaurelsprings

Answer: y > x + 4

Step-by-step 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!

semsee45

Answer:

[tex]\sf y > x+4[/tex]

Step-by-step explanation:

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

  • Let [tex]\sf (x_1,y_1)=(-4,0)[/tex]
  • Let [tex]\sf (x_2,y_2)=(0,4)[/tex]

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-0}{0-(-4)}=1[/tex]

point-slope form of linear equation:  [tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\implies \sf y-0=1(x-(-4))[/tex]

[tex]\implies \sf y=x+4[/tex]

Solid line : ≤ or ≥

Dashed line: < or >

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

[tex]\implies \sf y > x+4[/tex]

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