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Diffy said:If x is 10 can you give me a y such that y = x? If so that's the point (10,y)
If x is 12.3 can you give me a y such that y = x? If so that's the point (12.3,y)
If x is any value can you give me a y such that y = x? If so that's the point (x,y)
Do you see the solution now?
Diffy said: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?
HallsofIvy said: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?
LLS said: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.
steelphantom said: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.
LLS said: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.
steelphantom said: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.
BrendanH said:y=x is a straight line, at an elevation of 45 degrees from the x-axis, working counterclockwise. Plot that, and the answer will be however many times that graph and the line intersect.
HallsofIvy said: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)?
steelphantom said: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.
To find the values of x for which y=x on a graph, simply look for the points where the line y=x intersects with the x-axis. These points are the solutions or roots of the equation y=x.
The points of intersection represent the solutions or roots of the equation y=x. This means that when the value of x is equal to these points, the value of y will also be equal to this same point.
The number of values of x that satisfy the equation y=x on a graph will depend on the type of graph. In a linear graph, there will be infinitely many values of x that satisfy the equation y=x. In other types of graphs, there may be a finite number of solutions.
If the graph is a linear graph, you can use the points of intersection to find the solutions of the equation y=x. You can also use the slope of the line to determine additional solutions. In other types of graphs, you may need to analyze the shape of the graph and use algebraic methods to solve the equation.
Yes, there are other ways to represent the solutions of y=x besides a graph. These include algebraic equations, tables, and verbal descriptions. However, a graph is often the most visual and intuitive way to represent the solutions of y=x.