can you check my work?

- anonymous

can you check my work?

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- 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

@hartnn @surjithayer

- nincompoop

how did you solve for it?

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## More answers

- 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

so how did you pick that option ? I just want to know if you guessed or you did real math.

- 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

plug every point one by one and see which satisfy

- anonymous

im also looking for someone to show me how to do it

- anonymous

okay give me a sec

- 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

should i try doing it like surji said for now but give me one sec plz

- nincompoop

you can do it, but it seems that you need to understand beyond plugging in values.

- 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

okay so now that i have done it that way can you show me your way? nincompoop?

- nincompoop

my way is learning linear equation.

- anonymous

can you teach me if you don't mind>

- nincompoop

since your inequality has greater than or EQUAL to, we can start with equality \(y = mx + b \)

- anonymous

then what>|?

- 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

so so do you plug in like (0,4) then (2,0)?

- nincompoop

|dw:1433602878082:dw|

- nincompoop

brb. work-related

- ganeshie8

|dw:1433602934519:dw|

- 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

sounds awesome! :)

- anonymous

yupp but i have more questions i guess you guys can help with later

- 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

|dw:1433604121994:dw|

- nincompoop

|dw:1433604186698:dw|

- 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

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

so thats how y <= x + 3 looks in a graph?

- 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

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

|dw:1433605013888:dw|

- 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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