Why is it true that any two points satisfying a linear equation will
give you the same graph for the line represented by the equation?
2006-11-22 05:34:52 · 7 answers · asked by Ken H 1 in Science & Mathematics ➔ Mathematics
The equation is y= mx + b, where
m is the slope and b is the y - intercept.
As long as m and b remain constant, any values of x and y which satisfy the equation must produce the same line. This is because m and b by themselves define a unique line.
Easy example is to fix m =1 and b=0. We can say this is a line that passess through the origin, since b=0 and whose slope is 45 degrees, because arctan 1 =45 degrees. The equation is y=x and so all valuues such as (-50,-50), (0,0), and (,75,75) must lie on the line fixed by m and b because they satisfy x=y.
2006-11-22 05:53:46 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
Because when you meet those two points, you again draw a line which overlaps the line of equation.
You are just drawing a section of the line represented by the equation for all real values of the variables.
This would not happen in case of a parabola or a quadratic function.
If you have two points of the quadratic function ax**2+bx+c, they will not "give you the same graph for the line represented by the equation". This would be true for all non-linear functions.
I hope this helps.
2006-11-22 14:05:25 · answer #2 · answered by balsmin 3 · 0⤊ 1⤋
I believe it is because of the nature of a linear equation.
Any two points will form a line. A line is a graph of a linear equation. Therefore, if the two points in question satisfy the linear equation, they must, by definition, give you the graph of that equation (if you don't limit the graph to the points, if you do the it gives you the graph of the equation between those two limits)
2006-11-22 13:39:26 · answer #3 · answered by shinobisoulxxx 2 · 0⤊ 1⤋
Since the slope is a ratio of the change in height over the change in length, two points on a line will always contain that exact same ratio. The basic form of a line is y=mx+b where m is the slope. "b" is the y-intercept which also does not change. If you were to draw a line through the two points (which indeed is the actual line) you should eventually end up at the y-axis at the same y-intercept in the equation! Hope that helps!
2006-11-22 13:44:03 · answer #4 · answered by Jamison 1 · 0⤊ 1⤋
It's tautological. Any 2 points define a straight line.
If those 2 points satisfy the equation defining the line, self evidently, the points will be on the line.
2006-11-22 13:57:13 · answer #5 · answered by rosie recipe 7 · 1⤊ 0⤋
It will depend on what type of drugs you are on when performing the calculations. I was once told that the square root of 69 is 8 something.....but maybe not ?
2006-11-22 13:51:56 · answer #6 · answered by birdman 2 · 0⤊ 0⤋
Yes, because two points always define a line unambiguously.
2006-11-22 13:40:51 · answer #7 · answered by menezes_dean 2 · 0⤊ 1⤋