Question

Graph the following inequality and then select the correct graph below. y ≥ 3x - 3

Answer 1

Given the inequality:
`y\geq 3x-3`

The related equation for the given equation is:

y = 3x -3 ......[1]

x -intercepts: The point where the line crosses the x-axis

Substitute the value of y= 0 in [1] to solve for x;

0 = 3x -3

Add both sides 3 we get;

0 + 3 = 3x -3 +3

Simplify:

3 = 3x

Divide both sides by 3 we get;

`(3)/(3) = (3x)/(3)`

Simplify:

1 = x

or x = 1

x-intercept is (1 , 0)

y-intercepts: The point where the line crosses the y-axis

Substitute the value of x= 0 in [1] to solve for y;

y =3(0) -3 = 0-3

Simplify:

y = -3

y-intercept = (0 , -3)

When your inequality symbol:

• Greater than (>) or Greater than or equal to (
  `\geq`), then the solution region is above the boundary line.

• Less than (<) or Less than or equal to(
  `\leq`), then your solution region is below the boundary line.

Also, when the symbol is:

"> , < , then we draw a dashed line,

"
`\leq , \geq`", then we draw a solid line.

Since, the given inequality i.e
`y\geq 3x-3` symbol is
, draw a solid line and shade above the line:

As you can see the given inequality graph below in the attachment