Write a linear function if the graph passes through the point (2;4) and (-4;-2).
The equation of the linear function passing through the points (2,4) and (-4 , -2) is...
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We'll write the standard form of a linear function f(x):
f(x) = ax + b
In this case, the graph of the function is passing through the given points.
By definition, a point belongs to a curve if the coordinates of the point verify the equation of the curve.
(2;4) is on the line y = ax+b if and only if:
4 = a*(2) + b
2a + b = 4 (1)
(-4;-2) belongs to the graph of y = ax+b if and only if:
-2 = -4a + b
-4a + b = -2 (2)
We'll subtract (2) from (1)
2a + b + 4a - b = 4 + 2
We'll eliminate and combine like terms:
6a = 6
a = 1
From (1)=>2 + b = 4
b = 4 - 2
b = 2
The function f(x) whose graph is passing through the given points is:
f(x) = x + 2