Graph or explain how to graph on a coordinate plane: 4x + y ≥ 4

We have been given the inequality

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

First of all we graph the equation . 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.

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.