SOLUTION: Write a linear function where f(2)=4,f(4)=2 and f(3)=3.

Question 655658: Write a linear function where f(2)=4,f(4)=2 and f(3)=3.
Found 2 solutions by MathDazed, MathLover1:
Answer by MathDazed(34) (Show Source): You can put this solution on YOUR website!
The ordered pairs are (2,4) (4,2) (3,3)
You can find the slope = (3-2)/(3-4) = 1/-1 = -1
The equation would be y = -x + b
Subsitute one of the other ordered pairs into the equation
4 = -(2) + b
b = -6
The linear equation is y = -x-6
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
If ,, , then the graph of the function contains the point (,),(,), and (,).
Use the two point form of an equation of a straight line and the points (,),(,):
where (x1,y1)and (x2,y2) are the coordinates of the given points.

here is a proof that all three of given points lie on this line

Solved by pluggable solver: To determine if 3 points lie in a line

The 3 points lie on a same plane. For all points to lie on a line they should satisfy the equation of a line. Hence any two points taken on a line should calculate to the same slope of a line.

In order to prove the 3 points to lie on a line, as there exists a unique line containing three points and every line has a unique slope.
Hence it will be sufficient to prove that the slope calculated taking 2 points at a time should be equal.

Slope of line taking points (X1,Y1) and (X2,Y2) is

........................(1)

Slope of line taking points (X3,Y3) and (X1,Y1) is

........................(2)

From conditions (1) and (2)

The slopes are equal hence the 3 points can lie on same line.

If the slope calculated from points (X2,Y2) and (X3,Y3) comes out to be same then it is confirmed that the 3 points lie on a same line.

........................(3)

From (1),(2) and (3)

Hence, It is proved that the 3 points lie on same line.

To read more on equations of a line refer to articles on wikipedia

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