Question

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

Answer 1

Answer:

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;

$\frac{3}{3} = \frac{3x}{3}$

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 $"\geq"$ , draw a solid line and shade above the line:

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