Choosing axis when setting up Linear Inequality

Hi, I have a word problem that asks to set up an inequality and find possible solutions. I am able to get the right answer but have a questions about the axis. I am setting the inequality as S <= 30-6D. When I place S on the y axis, I get the same answer as the book. However, when I flip it and set S on the x axis, my graph looks different. So when I shade the region in both instances, i get different regions.

Does anyone know why this is the case? To me it seems that both ways should be right since choosing the axis where each variable goes on is arbitrary. Also, the scale of the y and x axis on the graph given by the book is not the same. The scale on the y axis is smaller than on the x axis.

The actual problem and graph are below.
Thanks so much!
Jon

Attachment 26748

A person is ordering helium balloons for his sister's birthday. He has up to $15 to spend. Decorative balloons cost $3 each and solid colored balloons cost $0.5 each.

a) Write an inequality to describe the situation.

b) Graph the solutions

c) Give two possible combinations of decorative and solid colored balloons the person can order.

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Originally Posted by jonathane40

Hi, I have a word problem that asks to set up an inequality and find possible solutions. I am able to get the right answer but have a questions about the axis. I am setting the inequality as S <= 30-6D. When I place S on the y axis, I get the same answer as the book. However, when I flip it and set S on the x axis, my graph looks different. So when I shade the region in both instances, i get different regions.

Does anyone know why this is the case? To me it seems that both ways should be right since choosing the axis where each variable goes on is arbitrary. Also, the scale of the y and x axis on the graph given by the book is not the same. The scale on the y axis is smaller than on the x axis.

The actual problem and graph are below.
Thanks so much!
Jon

Attachment 26748

A person is ordering helium balloons for his sister's birthday. He has up to $15 to spend. Decorative balloons cost $3 each and solid colored balloons cost $0.5 each.

a) Write an inequality to describe the situation.

b) Graph the solutions

c) Give two possible combinations of decorative and solid colored balloons the person can order.

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It doesn't make any difference which axis you choose for each variable.

Thanks, that's what I thought. I just graphed it on the computer and noticed that it''s the same graph, it is just oriented differently.

Thanks again!