anonymous
  • anonymous
can you check my work?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
To which graph does the point (2, 4) belong? y ≥ x + 3 y ≥ −x + 8 y ≥ 4x − 5 <--- my answer choice y ≥ −2x + 9
anonymous
  • anonymous
nincompoop
  • nincompoop
how did you solve for it?

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anonymous
  • anonymous
my brother showed me the way and i was seeing if its correct then if someone could show me the steps because he didn't explain it clearly
nincompoop
  • nincompoop
so how did you pick that option ? I just want to know if you guessed or you did real math.
anonymous
  • anonymous
no my brother did the math and told me the answer but im not sure because when he was explaining it it didn't make sense...
anonymous
  • anonymous
plug every point one by one and see which satisfy
anonymous
  • anonymous
im also looking for someone to show me how to do it
anonymous
  • anonymous
okay give me a sec
nincompoop
  • nincompoop
okay. There are different ways to do it, but it all starts with identifying the intercepts. Do you need a tutorial in identifying intercepts or do you already know it?
anonymous
  • anonymous
should i try doing it like surji said for now but give me one sec plz
nincompoop
  • nincompoop
you can do it, but it seems that you need to understand beyond plugging in values.
anonymous
  • anonymous
(2, 4) y ≥ x + 3 = 4 ≥ 2 +3 = 4 ≥ 5 which is false so its not A y ≥ −x + 8 = 4 ≥ -2 + 8 = 4 ≥ 6 which is false so not B y ≥ 4x − 5 = 4 ≥ 4(2) - 5 = 4 ≥ 8-5 = 4 ≥ 3 which is correct so it is C y ≥ −2x + 9 = 4 ≥ -2(2) + 9 = 4 ≥ -4 + 9 = 4 ≥ 5 which is false so not D
anonymous
  • anonymous
okay so now that i have done it that way can you show me your way? nincompoop?
nincompoop
  • nincompoop
my way is learning linear equation.
anonymous
  • anonymous
can you teach me if you don't mind>
nincompoop
  • nincompoop
since your inequality has greater than or EQUAL to, we can start with equality \(y = mx + b \)
anonymous
  • anonymous
then what>|?
nincompoop
  • nincompoop
The m is your slope. e b is your y-intercept - point where the value of the coordinate is (0, y). It means that the value of x is just zero (x = 0) and the value of y is anywhere -infinity and +infinity. So, pretty much the value of b is your actual y intercept |dw:1433602860664:dw|
anonymous
  • anonymous
so so do you plug in like (0,4) then (2,0)?
nincompoop
  • nincompoop
|dw:1433602878082:dw|
nincompoop
  • nincompoop
brb. work-related
ganeshie8
  • ganeshie8
|dw:1433602934519:dw|
anonymous
  • anonymous
she wants to teach me the way of doing it without plugging them in, and i want to know how to do it that way too
ganeshie8
  • ganeshie8
sounds awesome! :)
anonymous
  • anonymous
yupp but i have more questions i guess you guys can help with later
nincompoop
  • nincompoop
No, we cannot just do it like that. Next, is to identify the x-intercept. It is the point where it touches the x-axis, which also tells you that the value of y is zero (y=0). What this means analytically is to set your y to zero and solve for the rest of the equation. if you have \(y = x+3 \rightarrow 0 = x + 3 \) then solve for x, which in the example I showed you becomes: 0-3 = x + 3 - 3 -3 = x and your b is 3 so your intercepts are (0,3) and (-3, 0) |dw:1433604051743:dw|
nincompoop
  • nincompoop
|dw:1433604121994:dw|
nincompoop
  • nincompoop
|dw:1433604186698:dw|
nincompoop
  • nincompoop
suppose this is an inequality so that instead of y = x+3 we have \(y \ge x + 3 \) our linear equation is still the same, but the values of the points now are from anywhere the line lies and also above (greater). |dw:1433604445639:dw|
nincompoop
  • nincompoop
if instead the inequality is \(y \le x+3 \) then we shade the area of the region from where the line lies and the one below (less) it. |dw:1433604556647:dw|
anonymous
  • anonymous
so thats how y <= x + 3 looks in a graph?
nincompoop
  • nincompoop
correct! So, what we have covered so far are equality and inequality with greater than or equal to and less than or equal to. now, we need to do greater than or less than.
nincompoop
  • nincompoop
the good thing about this is that the still use the same LINE! meaning, that learning about linear equation in the slope-intercept form y = mx+b is quite helpful tool. now instead of including the line itself, we just need anywhere above (greater) or below (lesser). |dw:1433604945236:dw|
nincompoop
  • nincompoop
|dw:1433605013888:dw|
nincompoop
  • nincompoop
Now that you have an idea how the graph is like with linear equation and inequalities. We can determine if (2,4) is a point in the equation \(y\ge x+3 \) analytically. You can easily do this by "plugging in the values of x and y and see if it returns a TRUE value. Clearly, 4 is not greater than or equal to 5. And you do with the rest of the options. You can also do this graphically, but only if you have the patience to properly graph the equations and inequalities given. Never rely only on analytical solutions, because there will be problems where graphical understanding gives you a better intuition and idea how to attack a problem, and this is why I took the time to teach you the concept.

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