Question

find the equation of Best fit for the data in the table​

Answer 1

Answer:

The equation of the line is $y = 2\cdot x + 3$.

Step-by-step explanation:

The data of the table represents a line, also known as a linear function or a first order polynomial if and only if the following property is satisfied:

$\frac{y_{i+1}-y_{i}}{x_{i+1}-x_{i}} = m, m \in \mathbb{R}$ (1)

Now we proceed to check if the table represents a line instead of another kind of function:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{7-5}{2-1} = 2$

$\frac{y_{3}-y_{2}}{x_{3}-x_{2}} = \frac{9-7}{3-2} = 2$

$\frac{y_{4}-y_{3}}{x_{4}-x_{3}} = \frac{13-9}{5-3} = 2$

$\frac{y_{5}-y_{4}}{x_{5}-x_{4}} = \frac{15-13}{6-5} = 2$

Hence, the data represents a line. From Geometry we know that the equation of the line can be obtained by knowing two distinct points. The formula of the line is described below:

$y = m\cdot x + b$ (2)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$m$ - Slope.

$b$ - y-Intercept.

If we know that $(x_{1}, y_{1}) = (1, 5)$ and $(x_{2}, y_{2}) = (6, 15)$, then we have the following system of linear equations:

$m + b = 5$ (1)

$6\cdot m + b = 15$ (2)

The solution of the system of linear equations is: $m = 2$, $b = 3$.

The equation of the line is $y = 2\cdot x + 3$.