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y < – 4x – 2 y > – 4x – 2 y ≤ – 4x – 2 y < 4x – 2
Are you familiar with graphing inequalities?
No, not really.. I barely understand Algebra
Can you graph a standard line?
What math level are you currently on?
Before learning to graph inequalities, you are taught to graph lines and plot basic points. Correct?
I really don't know.. because I took half of Algebra like independent studies there was no teacher to explain what I was taking.
Btw, asalaam walikum and i hope Yemen will be freed soon.
Okay. So then i'd have to tutor you on graphing lines. Are you ready?
wa alaikum asalam, and in shaa Allah hopefully thanks
Let's began with the first multiple choice. y < – 4x – 2
Every line has an equation written similar to the slope intercept form. The slope intercept form of equation is written like this : \(\Large y=mx+b\) m stands for slopes b stands for y-intercept (where the line touches the y-axis and has a x=0) and x and y are changing, while m and b are constants.
When we have inequalities, we'll have to try to see if from a y=mx+b perspective so we can get a sense on what line we are dealing with. To do that, you basically change any inequality symbols (>, <) to an equal sign. So, \(\large y ~<~ – 4x – 2\) Will eventually become, \(\Large y=-4x-2\)
The line is y=-4x-2 Is this equation already in a slope intercept form?
what does it mean when you have ≤ this sign
If we have this, let's say \(y\le x\) That means all the y values are less than or equal to x are shaded and the line is straight and bold, not dashed. It would have been a dashed line if the symbols were just less than or greater than (<,>). But when we add an equal sign next to the inequality, than it becomes a bold line. So, when graphing it, it will become like this.|dw:1439489341719:dw||dw:1439489445470:dw|
As you can see from the graph i drew, all the y-values on the bottom of the line is shaded because the inequality is y is less than or equal to x.
And the line is bold, not dashed, because there's an equal sign with the inequality.
Now, back to graphing the first multple choice y = – 4x – 2 Can you graph this?
okay I'll try to
Thanks. I like when students participate on their problems. It gives me the sense that they are trying their best on their work.
You can try. Allah M3ek :)
am I right so far |dw:1439489802302:dw|
Yes, you drew the Cartesian graph correctly. Now, you can go ahead and draw the line. It's okay if you make any mistakes because you have me to correct it for you.
Everyone makes mistakes, including me :)
You can start by quickly plotting two points, and draw a line across those two points.
okay so can u help me now, im not sure what im supposed to do
That's the easiest way to do it. There's also other ways to draw a line.
Okay @proud_yemeniah_ are you familiar with plotting points?
I will plot one point, and you do the second point. Make sure you follow along. |dw:1439490142436:dw|
My first point is (0,-2) You can pick whatever you want for x, i chose 0 and got -2 for y, and you can choose 1 if you want.
so u just choose any number
Plotting points is all about choosing whatever number you want for x, and plug that number for x into the equation to get for y. Just like how I chose 0 and plugged that into y=-4(0)-2 and got -2 for y. Yes, you can choose any number.
What number would you like to choose?
so can I choose for example 3 or 2
Yes, whatever you want. What number will you choose?
I'll choose 2
plug that into the equation and tell me what you got for y
and i'll have to brb
okay, -4 (2) -2 ?
You can help me when u come back
I'm back. So you did: y=-4(2)-2 y=-8-2 y= ? what is y?
Yes. So we have two points. (0,2) and (2, -10) Can you plot these two points on this graph i drew? |dw:1439491250235:dw|
this is for the line y=-4x-2
I don't know how am I supposed to do it
Can you plot (2,-10)?
SOrry, i did something wrong
its okay, so -10 is Y?
yes, -10 is a y-value
(x,y) On a point, x is first, then y comes second.
Now, before you draw a line. Is the line dashed or bold in this inequality y < – 4x – 2 ?
Carefully look at the inequality symbol.
Yes. So, our two points that we plotted we \((0,-2)\) and \((2,-10)\) We plotted those. The line is dashed. |dw:1439492035470:dw|
What part of the graph is shaded, right or left?
y < – 4x – 2 y is less than -4x-2
I'll change the wording. Is the graph shaded on the top or bottom of the graph?
Does this look like the graph that was shown to you?
the right side was shaded
Nope. It doesn't doe A is incorrect. We know from the graph that the line is dashed, that means the inequality is show as < or > We also know that the line is positive because it continuously goes up to the right on the positive direction. The first choice y < – 4x – 2 went downwards because it was negative 4x-2. We also know that the graph is less than than or < because the graph is shaded on the bottom of the line.
From all those choices, which choice best fits the description.?
well if negative doesn't work then it may be D
I'm sorry if i have given you a hard time.
Now that you know how to graph a line and inequalities, then i have done my mission :)
Oh thank you very much.. No I actually liked going thru it and solving it together
Anytime. Good luck and take care!
You too thanks :) @Zale101