I need help understanding, how to graph the inequality, for the following story problem. On average, it takes an accountant 1 hour to complete a simple tax return and 3 hours to complete a complicated return. If the accountant wants to work no more than 9 hours per day, use the illustration to graph an inequality that shows the possible ways that simple returns (x) and complicated returns (y) can be completed each day. I got the inequality written write, which is x + 3y is equal to or less than 9..I just don't understand how to graph it..see attachment for solution from answer key..

Question

I need help understanding, how to graph the inequality, for the following story problem.  On average, it takes an accountant 1 hour to complete a simple tax return and 3 hours to complete a complicated return.  If the accountant wants to work no more than 9 hours per day, use the illustration to graph an inequality that shows the possible ways that simple returns (x) and complicated returns (y) can be completed each day.  I got the inequality written write, which is x + 3y is equal to or less than 9..I just don't understand how to graph it..see attachment for solution from answer key..

anonymous · Answer

I don't understand how the solutions manual came up with what they did...

a_clan · Answer

you probably  have doubt with the ordered pairs

anonymous · Answer

It's been a couple years since I've touched algebra at all...I'm in college now....I've forgot what the ordered pairs were all about, and how to find them...

a_clan · Answer

ordered pairs are pair of x, y values which satisfy  an equation.

You arbitrarily choose (preferably simple) values of x and put it in the equation to get corresponding values of y.

a_clan · Answer

since you are provided with an inequality, you treat it as an equation in order to calculate y-values
x+3y=9

anonymous · Answer

So I randomly put numbers in for x, which will give me different values for y...which will give me the graph that the solutions manual came up with? I guess I'm confused as to how their ordered pairs even correspond with the line they graphed..

a_clan · Answer

yes, that is how ordered pairs of (x,y) are calculated.
Now plot these point on graph.
draw a line passing through these points. 
It is the required graph

anonymous · Answer

I don't see a dot for any of the ordered pairs that they listed...their points appear to be within the shaded area to me...

a_clan · Answer

Because the ordered pairs they have provided is the part of final solution.
They are not on the line.

anonymous · Answer

The shaded area are all the points that satisfy the inequality. So it's ok if they points they give are in it. That's what you would expect.

anonymous · Answer

Any (x,y) value that is in the shaded region can be plugged in and you should get a true statement.

anonymous · Answer

For example if we take the (1,1) that they have:

$$1 + 3(1) \le 9 \implies 4 \le 9$$

Which is true. 4 is less than or equal to 9.

a_clan · Answer

Once you draw the line with the help of equation, then you see the condition of inequality, which states that x+3y be less than or equal to 9. So, any point below this line would satisfy the inequality. Hence, the solution is the shaded-area below the line.

anonymous · Answer

So how do I figure out the shaded area and line? this picture is from the answer key...

anonymous · Answer

The line is what you get when you consider the equality version of what you have. Instead of :
$$x + 3y \le 9$$
You look at this:
$$x + 3y = 9$$

anonymous · Answer

That last equation is a line. If you draw that line then you know where the edge of your inequality is.

anonymous · Answer

Since you want to consider only the points less than that line you shade the region beneath it.

anonymous · Answer

Any point in the shaded region will satisfy (make true) the original inequality.

anonymous · Answer

Would I have to put the x + 3y = 9 into y= x + ect. form?

anonymous · Answer

It probably makes it easier to graph that way yes.

anonymous · Answer

so does y = -(1/3) + 3 look right?

anonymous · Answer

It's missing an x, but other than that, yes. It's good.

anonymous · Answer

oops  the -1/3 was for the x..

anonymous · Answer

I figured =)

anonymous · Answer

But how can I graph this? The graph can't involve negative numbers...

anonymous · Answer

Welcome back to college btw =)

anonymous · Answer

Well like other graphs, you start with the y intercept. (3) then move according to the slope (down 1, right 3)

anonymous · Answer

Then draw a line between those two points.

anonymous · Answer

lightbulb finally came on..and I'm feeling pretty dumb now...

anonymous · Answer

You're doing great.

anonymous · Answer

I forgot that you start at the y intercept, not zero, with the 1/3  slope...

anonymous · Answer

One of the better students we've had around here in fact.

anonymous · Answer

um,I've hardly answered any questions on here, how can you say that?

anonymous · Answer

I said student, not tutor ;)

anonymous · Answer

funny...and plan to apply for a tutoring position at my college this fall...in math and science, lower levels anyway..:P

anonymous · Answer

That's awsome!

anonymous · Answer

So how long has it been since highschool?

anonymous · Answer

2 years.

anonymous · Answer

Oh, that's not bad at all. I waited 15 before I actually got around to going back to college.

anonymous · Answer

actually, this is my first time at college....I'm all caught up on doing good with my online algebra course...because grades mean everything, when trying for nursing..

anonymous · Answer

Yep. It's a good field to get into.

anonymous · Answer

well...I should get back to my math, thanks polpalk...I'll probably be back on here off and on all day today....I'm trying to get a lot of math done, so I can crash for my Anatomy and Physiology 1 test this Monday tomorrow...:P

anonymous · Answer

fun fun. =)

Good luck.