Given the point (2,3) and the function f(x) = (-m+1)x + 3, find what is m if the point lies to the graph of the function.
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We are given that (2,3) lies on the graph of the function f(x) = (-m+1)x + 3.
y = (-m+1)x + 3.
To determine m, substitute x and y from the point (2, 3)
3 = (-m+1)*2 + 3
=> 3 = -2m + 2 + 3
=> -2m + 2 = 0
=> 2m = 2
=> m = 1
The required value of m = 1
Since the point (2,3) is located on the graph of f(x), therefore, it must verify the given expression of f(x).
f(2) = 3
We'll replace x by 2 in the expresison of function:
f(2)=(-m+1)*2 + 3
Replacing x by 2, the function take the value of 3.
(-m+1)*2 + 3 = 3
We'll subtract 3 both sides;
(-m+1)*2 = 0
We'll divide by 2:
(-m+1) = 0
We'll isolate m to the left side:
-m = -1
m = 1
Therefore, for the point (2,3) to be located on the graph of f(x), m takes the value of 1.
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