Is the GCF (greatest common factor) of a pair of numbers ever equal to one of the numbers? Explain why or why not.
1 answer:
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Answer:
The easier way to solve this is to find the two points in the coordinate axis, and just draw a line that passes through the two points.
But let's be more complete:
Let's find the equations for each line:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
1) Here the points are (2,2) and (4,5)
then the slope is:
a = (5 - 2)/(4 - 2) = 3/2
y = (3/2)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (2, 2)
2 = (3/2)*2 + b
2 = 3 + b
2 - 3 = b
-1 = b
y = (3/2)*x - 1
2) Here the points are (0,1/2) and (2,3/2)
then the slope is:
a = (3/2 - 1/2)/(2 - 0) = 1/2
y = (1/2)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (0, 1/2)
1/2 = (1/2)*0 + b
1/2 = b
y = (1/2)*x + 1/2
3) Here the points are (-1,2) and (5,0)
then the slope is:
a = (0 - 2)/(5 + 1) = -1/3
y = (-1/3)*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-1, 2)
2 = (-1/3)*-1 + b
2 = 1/3 + b
2 - 1/3 = b
5/3 = b
y = (-1/3)*x + 5/3
4) Here the points are (-5,-3) and (-3,5)
then the slope is:
a = (5 + 3)/(-3 + 5) = -4
y = -4*x + b
And to find the value of b, we just replace the values of one of the points in the equation, in this case i will use (-3, 5)
5 = -4*-3 + b
5 = 12 + b
5 - 12 = b
-7 = b
y = -4*x - 7
Now that we have all the equations, we can find the graphs.
where the colors are:
(4) green
(3) orange
(2) Blue
(1) Gray.
