Question

Graph the following inequality and then select the correct graph below. x - y - 2 ≥ 0

Answer 1

the graph in the attached figure

Explanation:

we have

`x-y-2\geq 0`

Isolate the variable y

`-y\geq -x+2` -----> Multiply by
`-1`

`y\leq x-2`

The solution of the inequality is the shaded area below the solid line

The equation of the line is
`y= x-2`

The slope of the line is positive

The y-intercept of the line is the point
`(0,-2)`

The x-intercept of the line is the point
`(2,0)`

Using a graphing tool

the graph in the attached figure

Answer 2

To be able to graph any equation, simply solve for y.

You should get y ≤ x - 2
[the sign switched because you needed to divide by -1 in order to solve for y all the way]

Then use -2 as your y-intercept. This is the point that is at (0,y) on a graph. From the origin, just go down 2 points, and mark your point.

X is the same as 1/1 x. This is your slope. From point -2, rise 1 point, then run 1 point to the right (because it is positive). From that position, mark another point. You now have enough to make a line, which gives you the completed look of the graph for this equation.

It should look like this: