On the graph, for how many values of x does y=x?
The Attempt at a Solution
The obvious answer is (0,0).
There have to be more. I don't know how to go about finding this answer.
If x is 10 can you give me a y such that y = x? If so thats the point (10,y)
If x is 12.3 can you give me a y such that y = x? If so thats the point (12.3,y)
If x is any value can you give me a y such that y = x? If so thats the point (x,y)
Do you see the solution now?
I'm sorry, I didn't see that there was an attachment. I thought your question was a bit easier. Your attachment awaits approval, can you describe it for me?
You've certainly got me confused! What lines did you draw at (1,1), (2,2), etc.?
I have no idea what you are talking about when you say "At 0, there are 3"! What do you mean "at 0"? Do you mean "at (0,0)" or "at x= 0" or "at y=0"? And there are 3 what?
The problem is asking "where does this graph cross the line y= x?" That's difficult to answer here because it depends strongly on how accurate this graph is supposed to be and exactly where each end of the "S" ends. Can you draw the line y= x?
Yes, at (0,0)
I don't understand what you mean by the line y=x. I don't know where to draw it, or how/why it's just one line.
I am sorry to confuse you. Things get lost in translation in this format.
I'm not getting the concept but I am trying hard.
The line y = x consists of all the points where *drumroll...* y = x. For example, (0, 0), (1, 1), (2.439, 2.439), etc. Plot two of these points on the graph (maybe (0, 0) and (1, 1) ). The straight line that connects these points is y = x. It extends out infinitely past both points.
I sort of understand that. But I still don't understand what the answer is.
How many are there? It seems that the number is infinite.
The number of points on the line y = x is infinite, but the number of points where the line y = x intersects your "S" is not. Draw the line y = x as well as the "S," and the points where the lines cross will be the intersection points.
For example, in http://education.yahoo.com/homework.../1/minialg2gt_12_1_1_27_110/f-438-1-we-1.gif", there are two points where the line intersects the ellipse.
Good! How did you come up with that? I presume you have a clearer picture than we can see on the internet, because I was not at all sure. (Of course, I didn't want to draw on my computer screen!) Obviously, as you said, (0,0) is one point of intersection. Is the other in the lower left (3rd quadrant) or upper right (1st quadrant)?
If you look at the graph (the image has finally been approved), you will see that the origin and also the two end points of the S all lie on the line y = x, so there are actually 3 points that the line y = x intersects. The end points of that graph should really be labeled, though.