Question

http://prntscr.com/99ejg2

Answer 1

@Directrix

Answer 2

I would suggest you represent the bounding line that divides the solution plane with the non-solution one.
For that, we will find all the points that satify: \(y=-\frac{ 3 }{ 4 }x+3\)
And this is the equation of the line written in it's explicit form, if you have trouble representing a line by it's equation, you can spot two points by giving any value to "x" and solving for "y".

Just to repeat myself a little, we must first find the boundry line of the divided planes, for that we turn the inequality sign into an "=" sign.

Answer 3

http://prntscr.com/99emey

is this correct?

Answer 4

Good, now, in order to see what region will determine the solution, we pick any point not belonging to the line and plot it in, operate the corresponding operations and if the inequality is satisfied then the point must belong to the solution region.
For this, people use most commonly the origin, so by that I mean you plot the point (0,0) in the inequality: \(y \le -\frac{ 3 }{ 4 }x+3\)

Answer 5

http://prntscr.com/99eoju

like that?

Answer 6

Yes, you represented the point, but I want you to insert it into the inequality, what you do is replace the x,y values of the point to the inequality:
\[y \le -\frac{ 3 }{ 4 }x+3\]
\[0 \le -\frac{ 3 }{ 4 }(0)+3\]

Answer 7

http://prntscr.com/99epre

Answer 8

That is correct.

Answer 9

is that all i have to do?

http://prntscr.com/99eqc1

Answer 10

No, you have to simplify the expression:
\[0 \le -\frac{ 3 }{ 4 }(0)+3\]
it ends with:
\[0 \le 3\]
And zero is less than three so that means that the origin actually is a point belonging to the solution plane.

Answer 11

http://prntscr.com/99f29f

is this correct for part b?

Answer 12

@Directrix

Answer 13

Okay, I see your graph. It is correct.

Answer 14

(1,2) is in the solution set and means 1 pound of apples and 2 pounds of oranges which the girl can buy for a total cost which is less than $12.

Answer 15

Repair part B. (4,3) is not part of the solution set.

@Diana.xL

Answer 16

thnx

Answer 17

You are welcome.