Which Kind Of Function Best Models The Set Of Data Points (-1 22)

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Question 947844: Which kind of function all-time models the set of data points:
-ane,22 0,6 1,-10 ii,-26 and three,-42?
linear
quadratic
exponential
non east of the higher up

my answer is linear
Answer by MathLover1(19486) (Show Source):
You tin can put this solution on YOUR website!
first check if they lie in a line:

Solved by pluggable solver: To decide if three points prevarication in a line

The iii points prevarication on a same aeroplane. 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 club to show the 3 points to lie on a line, equally 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 ii 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

........................(two)

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 exist same then it is confirmed that the 3 points lie on a aforementioned line.

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

From (1),(two) and (3)

Hence, It is proved that the 3 points prevarication on aforementioned line.

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

Solved by pluggable solver: To make up one's mind if three points prevarication in a line

The 3 points lie on a same aeroplane. For all points to prevarication on a line they should satisfy the equation of a line. Hence any ii points taken on a line should calculate to the aforementioned slope of a line.
In society to bear witness the 3 points to lie on a line, every bit in that location exists a unique line containing three points and every line has a unique gradient.
Hence information technology volition exist sufficient to show 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 weather (i) and (2)

The slopes are equal hence the iii points can lie on aforementioned line.

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

........................(three)

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

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

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

since all points prevarication in a line, choose 2 of them and find linear equation:

Solved past pluggable solver: Find the equation of line going through points

hahaWe are trying to discover equation of course y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (i, -ten) and (x2, y2) = (0, vi).
Slope a is .
Intercept is found from equation , or . From that,
intercept b is , or .
y=(-16)ten + (vi)

Your graph:

then, reply is: linear