All points on this line will have the same slope in between them.
You actually can tell what the slope is from looking at the equation. The equation is in slope-intercept form, "y = mx + b" where m is the slope and b is the y-intercept.
On the basis of that, we know that the slope is 2. We can verify this by finding two points and looking at the slope between them.
Let's choose two easy ones - x = 0 and x = 1
At x = 0, y = 2(0) +3 so y = 3 - so that's one ordered pair: (0,3)
At x = 1, y = 2(1) + 3 so y = 5 - that's another ordered pair: (1, 5)
The slope between two points can be found by subtracting the y coordinates and dividing that by the difference in the x coordinates (rise over run). Generally this looks like (y2-y1)/(x2-x1).
In this example: (5-3) / (1-0) = 2/1 = 2
This is consistent with my earlier claim that the slope is 2. Since lines extend infinitely there are an infinite number of pairs of points whose slope in between them will be, for this line, 2.
2007-11-10 07:55:18
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answer #1
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answered by Rock R 3
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to find two points just place a value in the equation for (x) and you will get ( y )
f(x) = 2 ( 2 ) + 3 = 7 for x=2 point is ( 2,7)
f(x) = 2 ( -2) + 3 = -1 for x = -2 point is ( -2 , -1)
for the slope the derivative of f(x) ' = slope
d/dx = 2 slope is = 2
y = 2x + 3 is in the slope intercept form y = mx + b
and m is the slope m = 2
Also Slope is (y2-y1) / x2-x1) = [7-(-1)] /[( 2-(-2)] = 2
2007-11-10 07:56:17
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answer #2
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answered by ? 3
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To find two points, pick two values for x:
x=0, 2
Then, solve for each x value:
f(0)=2(0)+3
f(0)=3
f(2)=2(2)+3
f(2)=7
Therefore, our two points are:
(0,3) and (2,7)
To find the slope between these points, use the definition of slope:
slope=change in y divided by change in x
slope=(y2-y1)/(x2-x1)
slope=(7-3)/(2-0)
slope=4/2
slope=2
2007-11-10 07:54:46
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answer #3
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answered by RoboPaul 3
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If x = 0, f(x) = 3 so (0,3) is a point
If x = 1, f(x) = 5, so (1,5) is a point
So slope = (5-3)/(1-0) = 2/1 = 2
2007-11-10 07:53:21
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answer #4
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answered by ironduke8159 7
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when x = 1 f(1) = 5
when x = 2 f(2) = 7
so your two points can be (1,5) and (2,7)
slope = (y2-y1)/(x2-x1) = (7-5)/(2-1) = 2
slope from an eq with mx + b is m, so it is 2
2007-11-10 07:52:38
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answer #5
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answered by norman 7
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pick two numbers. Plug the first number in for x and work it out. this will be the first point. Now, do the same for the second number you picked, and this will get you the second.
Plug into the formula (y2- y1)/(x2- x1). X1 will be your first x that you plugged in, y1 will be your first answer. x2, is the second x, and y2 is the second answer you got from above.
2007-11-10 07:54:11
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answer #6
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answered by hh 1
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