-6x+8y<4

Add 6x to both sides of the inequality.

8y<4+6x

Divide each term by 8 and simplify.

Divide each term in 8y<4+6x by 8.

8y8<48+6×8

Cancel the common factor of 8.

Cancel the common factor.

8y8<48+6×8

Divide y by 1.

y<48+6×8

y<48+6×8

Simplify each term.

Cancel the common factor of 4 and 8.

Factor 4 out of 4.

y<4(1)8+6×8

Cancel the common factors.

Factor 4 out of 8.

y<4⋅14⋅2+6×8

Cancel the common factor.

y<4⋅14⋅2+6×8

Rewrite the expression.

y<12+6×8

y<12+6×8

y<12+6×8

Cancel the common factor of 6 and 8.

Factor 2 out of 6x.

y<12+2(3x)8

Cancel the common factors.

Factor 2 out of 8.

y<12+2(3x)2(4)

Cancel the common factor.

y<12+2(3x)2⋅4

Rewrite the expression.

y<12+3×4

y<12+3×4

y<12+3×4

y<12+3×4

y<12+3×4

y<12+3×4

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 12 and 3×4.

y<3×4+12

Rewrite in slope-intercept form.

y=34x+12

y=34x+12

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=34

b=12

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

Slope: 34

y-intercept: 12

Slope: 34

y-intercept: 12

Slope: 34

y-intercept: 12

Graph a dashed line, then shade the area below the boundary line since y is less than 12+3×4.

y<12+3×4

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