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so a friend of mine is asking for help but i don't really remember much of my algebra days :/
so, what's the question?
ok so first he was asked to draw a flag one sec let me draw it
ok so lets get to the problem
he os asked to show these points in y=mx+b and in standard form
but if we already have all the x y's what do i do ; ;
maybe he's supposed to write equations for those lines that make up the diagram?
hmm how would i go about doing this? he isnt really that familiar with the material :/
Well, the vertical and horizontal lines are pretty easy. For example, the bottom line is a horizontal line that passes through (-5,-3) and (5,-3). We know the slope is 0, so it is just \[y=k\] for some value of \(k\), right? Doesn't matter what value of \(x\), \(y\) is always -3 for that line.
Similarly, any vertical lines are just \[x=k\]for some value of \(k\), because all the \(x\) values are the same, and only the \(y\) value changes.
1. draw the flag out in graphing paper, graph must include coordinates and labled increments plot each point at the end of each line segment on the flag for each line creat a table with four points write an equation in slope intercept and standard and list the domain and range
those are the instructions
Now, the "slanted" lines are probably what the problem author is interested in...there we know two points the line passes through, and from that, we can determine the equation of the line.
okay, yeah, looks like what I guessed. Let's take that line from \((-5,-3)\) to \((0,0)\) as an example. The domain is going to be -5 to 0, inclusive; those are the values that \(x\) is allowed to take. \[-5\le x\le 0\]is another way you could write that. The range is the range of values \(y\) can have over the domain. At the minimum, \(y=-3\) and at the maximum, \(y = 0\), so we could write the range as \[-3\le y \le 0\] Any question about that?
let me show you what i just did
and i still have trouble with domain and range
yes, put 4 points in that table, different values of x, all the same value of y, and you have your table. Now domain is the set of allowed values of x (the independent variable), and range is the set of resulting values of y (the dependent variable). For this line segment, how would you describe the allowed values of x?
hmm you lost me xD. but the allowed values reffer to the x then wouldnt they be -5 to 5 because thisline goes from -5 to 5?
exactly. "domain" is just a fancy term to confuse you :-)
and for range?
isn't there only one possible y value for this line?
what do you mean?
i think i just made sense of it, the range would be 5 xD
no, the range is 3, isn't it? isn't y = 3 for all values of x for that line?
oh yea i was refering to his table xD
i made my own so i can help him xD
Thank you SOOOOOOOOOO much.
glad I could help you help your friend :-)
I find that explaining something to someone else is a really good way to reinforce your own knowledge.