x+2y<8

Subtract x from both sides of the inequality.

2y<8-x

Divide each term by 2 and simplify.

Divide each term in 2y<8-x by 2.

2y2<82+-x2

Cancel the common factor of 2.

Cancel the common factor.

2y2<82+-x2

Divide y by 1.

y<82+-x2

y<82+-x2

Simplify each term.

Divide 8 by 2.

y<4+-x2

Move the negative in front of the fraction.

y<4-x2

y<4-x2

y<4-x2

y<4-x2

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 4 and -x2.

y<-x2+4

Rewrite in slope-intercept form.

y=-12x+4

y=-12x+4

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=-12

b=4

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

Slope: -12

y-intercept: 4

Slope: -12

y-intercept: 4

Slope: -12

y-intercept: 4

Graph a dashed line, then shade the area below the boundary line since y is less than 4-x2.

y<4-x2

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