Respuesta :

We have been given the inequality

[tex]4x + y \geq  4[/tex]

In order to graph this inequality, we will follow below mentioned steps:-

  • First of all we graph the equation [tex]4x + y = 4[/tex]. The x-intercept of the line is 1 and the y-intercept is 4. Hence, this line must pass through the point (1,0) and (0,4)
  • Now, since we have greater than equal to sign hence the line must be solid.
  • Now, we have to decide which region we need to shade and for this we apply the origin test.
  • Substituting x=0 and y=0 in the given inequality and check if the condition holds true or not.

[tex]4 \cdot  0+0 \geq 4\\ \\  0+0 \geq 4\\ \\ 0 \geq 4\\[/tex]

Since 0 cannot be greater than 4. Hence, the condition is False.

  • Hence, we will shade away from origin.

Using all the above mentioned concepts, we can graph the inequality.

Attached is the graph of the inequality.

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