Question

Help! math problem step by step please

Answer 1

Answer:

2x -y ≥ 4

Step-by-step explanation:

The intercepts of the boundary line are given, so it is convenient to start with the equation of that line in intercept form:

... x/(x-intercept) + y/(y-intercept) = 1

... x/2 + y/(-4) = 1

Multiplying by 4 gives the equation of the line.

... 2x -y = 4

This line divides the plane into two half-planes. The half-plane that is shaded is the one for larger values of x and/or smaller values of y than the ones on the line. So, for some given y, if we increase x we will get a number from our equation above that is greater than 4. Hence, the inequality we want is ...

... 2x -y ≥ 4

We use the ≥ symbol because the line is solid, so part of the solution space.