- Something I struggled with figuring out how to do in Unit 3 would be graphing linear inequalities. With this I would get confused on how to shade the graph properly. At first I didn’t know that you were supposed to test (0,0) on the graph unless 0 was involved in your equation, then you would use (1,1) to see how to shade. If your equation was true when you tested it out with (0,0) for example, then, you would shade the portion that included (0,0).
2. Example Question:
Nick is preparing a tomato and red pepper soup as the daily special for his restaurant.
-To allow the red pepper taste to dominate, he will include at least twice as many peppers as tomatoes, by mass.
-However, he wants no more than 25 kg of tomatoes and red peppers altogether.
a) Define the variables and write a system of inequalities to model this situation.
b) Graph the system.
3. Youtube Video:
4. 
For part a in the equation I first determined my variables, by representing x as tomatoes by mass and y as red peppers by mass.
Then I had to put it into an equation so I could graph it on the graph. For when it said: to allow the red pepper taste to dominate, he will include at least twice as many peppers as tomatoes, by mass. For this you have to realize there is twice as many peppers as tomatoes, so you would have to multiply the tomatoes by 2 to get the peppers so I made the equation 2x≤y. It then said however, he wants no more than 25 kg of tomatoes and red peppers altogether so you would have to understand that since he wants no more than 25 kg of tomatoes and red peppers altogether you would have to put 25 is greater than or equal to tomatoes by mass + red peppers by mass, which would give you the equation: 25≥x+y
For part b in this equation I had to graph the equation. First, I had to put the equation in y=mx+b form so for 2x≤y, I would get y≥2/1x+0 because first you would want y at the beginning so it would be y≥2x. Next, since 2x is by itself and is not divided by anything, you should know that you divide it by 1 so it would now be y≥2/1x. Last, there is no variable for b so you would just substitute b in for 0, so your final equation would equal to y≥2/1x+0. For the next equation I would also have to put it in y=mx+b form so for 25≥x+y, it would equal y≤-1/1x+25. To get this you would first, have to get y by itself, and to do this you would have to move x to the other side so it is with 25 so your equation would now be -x+25≥y. Next, in my preference you would have to flip the equation over so it would be y≤-x+25. I do this because I prefer having y at the beginning of the equation. Finally you have to understand that since it is -x it would equal out to -1/1 x because it is -x so it is -1 and you would divide it by 1 since it doesn’t specify you to divide it by anything, so you would get the final equation of y≤-1/1x+25. Now that you have both of the equations in the proper format, you have to test them out to see if you should shade within (1,1) or not. For the first equation of y≥2/1x+0 you would test it out with (1,1) so you would get 1≥2/1(1)+0 which would then equal 1≥2 which is false so you would not include (1,1) in the shading area. Next, I tested it out with the other equation of y≤-1/1x+25 and substituted in (1,1) so the equation was 1≤-1/1(1)+25. Doing the math on this you would get the answer of 1≤24 which is true so you would involve (1,1) in the equation. Tomatoes = blue, Red peppers= green, and both of them = dark blue. For sketching the equation on the graph you start at 0 for y≥2/1x+0 and go up 2 over 1 because it is rise over run. You also do the same for y≤-1/1x+25, except you start at 25 on y this time and go -1 down and 1 over to the right because rise over run as well.
5.
-What misconceptions did you have previously that made this skill challenging?
The misconceptions I had previously, before figuring out this skill was to test out the points with either (1,1) or (0,0) to see if the answer was true or false. At first I did not understand the shading but after figuring out the true or false part it made a lot more sense to me and I always remembered to shade every one lightly after that because 1 of the sections will contain both so you have to use a different colour for it.
-What key things did you learn?
I think the biggest and most important thing that I learned this unit that helped me out with the test is just being able to test it to see if it is true or false because with that knowledge you are basically getting an extra 2 marks for showing your work for true and false and shading the graph properly, so if I did not know this skill I would have got 2 marks off on every kind of question like this one.
-How does this connect to other skills/concepts in the unit?
It is all together in one unit so everything has to do with each other. If you did not have the testing points, you would not be able to shade the graph in properly and like I said before you would get 2 marks off on the question. I think if you know how to test the points out though and fully understand it, it will help you out a lot with this unit.