How do you graph the inequality #y>= x+4# and #y >6x-3#?

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Answer 1 · 2017-07-23T22:15:43

When it is #>=#, make the line solid and shade in above the line. When it is just #>#, make the line dashed and shade in above the line.

Draw a solid line, #y = x + 4#, by placing a straight edge along the points #(0,4)# and #(-4,0)#:

![www.desmos.com/calculator]( useruploads.socratic.org )

To obtain a graph of the #x >=x+4#, shade in the area above the line:

![www.desmos.com/calculator]( useruploads.socratic.org )

Draw a dashed line, #y = 6x -3#, by placing a straight edge along the points #(0,-3)# and #(1/2, 0)#:

![www.desmos.com/calculator]( useruploads.socratic.org )

Shade in the area above the line:

![www.desmos.com/calculator]( useruploads.socratic.org )

The magenta region is the region that makes both inequalities be true.