-3x-2y>6

Add 3x to both sides of the inequality.

-2y>6+3x

Divide each term by -2 and simplify.

Divide each term in -2y>6+3x by -2. When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

-2y-2<6-2+3x-2

Cancel the common factor of -2.

Cancel the common factor.

-2y-2<6-2+3x-2

Divide y by 1.

y<6-2+3x-2

y<6-2+3x-2

Simplify each term.

Divide 6 by -2.

y<-3+3x-2

Move the negative in front of the fraction.

y<-3-3×2

y<-3-3×2

y<-3-3×2

y<-3-3×2

Rewrite in slope-intercept form.

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Reorder -3 and -3×2.

y<-3×2-3

Rewrite in slope-intercept form.

y=-32x-3

y=-32x-3

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y=mx+b.

m=-32

b=-3

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: -32

y-intercept: -3

Slope: -32

y-intercept: -3

Slope: -32

y-intercept: -3

Graph a dashed line, then shade the area below the boundary line since y is less than -3-3×2.

y<-3-3×2

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