Question

How do you graph `72\geq - 3x - 6y`?

Answer 1

See the process in the explanation.

Explanation:

Rearrange the equation into slope intercept form.

`72>= -3x-6y`

Add `6y` to both sides.

`6y+72>=-3xcolor(red)cancel(color(black)(-6y))color(red)cancel(color(black)(+6y)`

Simplify.

`6y+72>=-3x`

Subtract `72` from both sides.

`6ycolor(red)cancel(color(black)(+72))color(red)cancel(color(black)(-72))>=-3x-72`

Simplify.

`6y>=-3x-72`

Divide both sides by `6`.

`y>=-3/6x-12`

Simplify.

`y>=-1/2x-12` `lArr` Slope intercept form

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Determine points for `y>=-1/2x-12`

`x=0,` `y=-12`
`x=2,` `y=-13`
`x=4,` `y=-14`
`x=6,` `y=-15`

Plot the points and draw a straight, solid line through the points. Shade the above the line. graph{y>=-1/2x-12 [-13.96, 18.08, -20.63, -4.61]}