CyberStein wrote:
Quote:
y = 2x is the equation of the line - fine.
But these two - (3,y) and (x,4) are points. Here y and x are specific co-ordinate points.
Think of them instead as points (3, a) and (b, 4). You need to find a + b.
You will get 10 = 2a + b by equating it to slope but how will you solve for a + b?
The equation of the line is y = 2x
So a = 2*3 = 6
Also, 4 = 2*b
b = 2
So a + b = 6 + 2 = 8
I got the question at hand right (C), but I am uncomfortable as to how I got it right -- it felt like guessing.
here is what I did, step by step:
1. y = mx + b
2. y = 2x + 0 given slope = 2, and the origin
3. y = 2x
After step three, I dead ended and did not know how to use "y = 2x" to solve for the missing points.
So, I just looked at the problem from a rise over run POV
2 = rise / run
2 = y-4 / 3-x <--- right here, I essentially guessed by plugging in numbers until the equation worked.
2 = (6) - 4 / 3 - (2) <--- I plugged in 6 for Y and 2 for X because I knew it would give me 2; however, I know that this way is essientially guessing.
What is a simplified solution to the problem, following the steps I followed?
CyberSteinYou had it! I think you just forgot that you already found the relationship between y and x (in the equation) -- and, once you have the linear function in the form of the equation, you can find one coordinate if you have the other.
The missing x and y have nothing to do with one another except that they are on the same line. The question is asking for one more trivial step after you do the work: can you track correctly and add?
All you need to do: use the line equation you found, take one pair of coordinates at a time, and plug in the given value to find the missing one.
For (3,y). We know THIS x is 3. What is its matching y-coordinate? Plug in the given x-value to find the y-value for
this pair. We need the "missing" y in (3,y).
y = 2x
Given: x = 3. Plug it in.
y = (2)(3)
y = 6
y equals 6 when x equals 3. The pair is now (3,
6).
If you were graphing, and went to x equals 3, you would go up to y equals 6.
Now the other pair. We are given (x,4). We need x.
y = 2x
Given: y = 4. Plug it in.
4 = 2x
4/2 = x
x = 2
For this pair we have (
2,4).
This pair is a little odd because we are used to thinking of y as a function of x, and not the other way around. But we already have the relationship between y and x. It's in the equation you wrote.
The question at the end is trivial, meaning, it has nothing to do with the relationship between the x and the y -- except what a randomly picked x-value and a randomly picked y value, from that line, add up to.
The question is, my rewrite: "[Now that you have figured out the line equation, and figured out particular values for missing coordinates from two different pairs], what does [that] x + [that] y equal?"
We got x equals 2 on the one hand, and y equals 6, on the other hand. Add them.
2 + 6 = 8
Maybe you were thinking too hard, that's all. I should all have such problems!
I couldn't quite tell where you were going wrong, so I guessed. Does that help?
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