How would I graph this inequality?
2.5x + 2.5y

Question

How would I graph this inequality? 
2.5x + 2.5y <= 1000

anonymous · Answer

Solve for y, graph that line, figure out whether to shade above or below it.

anonymous · Answer

Does that include x also?

whpalmer4 · Answer

If you solve for $y$ as suggested, you'll get an equation in terms of $x$.  Graph that line, then pick a convenient test point.  I always use (0,0) because it almost always guarantees easy arithmetic.  If (0,0) satisfies the inequality, you shade the side that contains (0,0).  If it doesn't satisfy the inequality, you shade the other side.  Does that make sense?

anonymous · Answer

So I got x <= -y + 400, I am still confused on how to graph it.

whpalmer4 · Answer

Okay, here's how I would do it:
$$2.5x+2.5y \le 1000$$Turn it into an equality
$$2.5x+2.5y=1000$$Divide everything by 2.5 to get $y$ with no coefficient$$x+y=400$$Subtract $x$ from both sides to get expression for $y$ in terms of $x$
$$y=400-x = -x + 400$$Okay, we know from examining that equation that it is a line with slope = -1 and it crosses the y-axis at y=400.  This we get from slope-intercept form:
$$y=mx+b$$$m$ is slope, $b$ is y-intercept value.
We can find where it crosses the x-axis (x-intercept value) by setting $y=0$ and solving for $x$:
$$0=-x+400$$$$x=400$$
So now we have two points, (0,400) and (400,0), and we just draw a straight line through them.  That's our graph.  Pretty easy, right?  Now, we try out my favorite test point (0,0) in the original inequality and see which side we'll be shading.
$$2.5(0) + 2.5(0) \le 1000$$Is that true?

whpalmer4 · Answer

By the way, we use a solid line for our graph because the inequality includes the equals sign.  That means the points on the dividing line are included.  If not, we would use a dashed line to signify that they are not.

anonymous · Answer

I see, thanks for the help. But I am supposed to have a graph such as the attachment.

whpalmer4 · Answer

Yeah, so?  You only supplied one equation, you aren't going to have three constraints like the graph in the attachment does.

whpalmer4 · Answer

Sorry, one inequality, not one equation.

anonymous · Answer

Ah, yea, I am dumb... I wasn't even thinking about that. Sorry...! :S