Write a linear function if the graph passes through the point (2;4) and (-4;-2).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the linear function passing through the points (2,4) and (-4 , -2) is a straight line given by

y + 2  = [ (4 + 2) / (2 + 4)]*( x + 4)

=> y + 2 = (6/6)*(x + 4)

=> y + 2 = x + 4

=> y = x + 2

Or f(x) = x + 2

The required linear function is f(x) = x + 2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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