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To which graph does the point (2, 4) belong? y ≥ x + 3 y ≥ −x + 8 y ≥ 4x − 5 <--- my answer choice y ≥ −2x + 9
how did you solve for it?
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
so how did you pick that option ? I just want to know if you guessed or you did real math.
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...
plug every point one by one and see which satisfy
im also looking for someone to show me how to do it
okay give me a sec
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?
should i try doing it like surji said for now but give me one sec plz
you can do it, but it seems that you need to understand beyond plugging in values.
(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
okay so now that i have done it that way can you show me your way? nincompoop?
my way is learning linear equation.
can you teach me if you don't mind>
since your inequality has greater than or EQUAL to, we can start with equality \(y = mx + b \)
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|
so so do you plug in like (0,4) then (2,0)?
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
sounds awesome! :)
yupp but i have more questions i guess you guys can help with later
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|
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|
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|
so thats how y <= x + 3 looks in a graph?
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.
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|
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.