Question 947844: Which kind of function best models the set of data points:
-1,22 0,6 1,-10 2,-26 and 3,-42?
linear
quadratic
exponential
non e of the above
my answer is linear
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! first check if they lie in a 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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| 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
|
since all points lie in a line, choose two of them and find linear equation:
| Solved by pluggable solver: Find the equation of line going through points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (1, -10) and (x2, y2) = (0, 6).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is  , or  .
y=(-16)x + (6)
Your graph:
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so, answer is: linear
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