Question

Find the linear approximation of the data that passes through the points (5, 3) and (20, 6). y = 15x + 9 y = 15x + 3 y=1/5x-1 y=1/5x+2

Answer 1

y=1/5x+2

Explanation:

In order to be able to calculate the solution for this problem you just have to evaluate the equations for one of the point that you are given by inserting the valueof X and if it gives as a result the value of Y you have the function that is correct or that passes through those points:

Point (5,3)

y = 15x + 9/ 3=15(5)+9/3=45+9/3=54

As you can see the equation is not equal, so it´s not true, this eliminates also the next one.

y=1/5+2/3=5(1/5)+2/3=1+2/3=3

This is correct for the first point we have to evaluate it for the second point:

(20,6)

y=1/5+2//6=20(1/5)+2/ 6=4+2/6=6

So since it is equal the function is correct.

The functions that passes through the points (5,3) and (20,6) is y=1/5+2

Answer 2

If you try the given points in the offered equations, you find the only equation that makes sense is ...
y = 1/5x +2

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If you want to determine the equation yourself, you can use the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)*(x -x1) +y1
y = (6 -3)/(20 -5)*(x -5) +3
y = 3/15*(x -5) +3
y = 1/5x -1 +3
y = 1/5x +2