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Question 799968: How do you rewrite these equations in Function Form:
-3x+y=12
2x+3y=6
-x-y=5
Answer by thepianist25(8)   (Show Source):
You can put this solution on YOUR website! To write these equations in function form, first change them to slope-intercept form.
Slope intercept form is "y = mx + b", where m is the slope of a line, x and y are the coordinates, and b is the y-intercept. Once you have solved for y, then you can can simply substitute "f(x)" in place of y, to show that it is in function form (which you could graph).
So, in -3x + y = 12, I must solve for "y".
-3x + y = 12
-3x + 3x + y = 12 + 3x (addition axiom)
y = 3x + 12
Notice that we are in slope-intercept form. You can now change the equation to f(x) = 3x + 12
The other two equations are done the same way.
2x + 3y = 6
2x - 2x + 3y= 6 - 2x (subtraction axiom)
3y = -2x + 6
3y/3 = -2x/3 + 6/3 (division axiom)
y = -2x/3 + 2 or f(x) = -2x/3 + 2
-x - y = 5
-x + x - y = 5 + x (addition axiom)
-y = x + 5 (At this point, I do not want to leave y with a negative on it. So if I divide both sides by -1, I will not destroy the equality of the equation.)
-y/-1 = x/-1 + 5/-1
y = -x - 5 or f(x) = -x - 5
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