Question

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

Answer 1

We have been given the inequality

$4x + y \geq 4$

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

• First of all we graph the equation $4x + y = 4$. 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.

$4 \cdot 0+0 \geq 4\\ \\ 0+0 \geq 4\\ \\ 0 \geq 4$

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.