Answer:
Option C is the answer.
Step-by-step explanation:
To find the equation of the straight line equation i.e, we must be given with the two points [tex]\left (x_{1},y_{1} \right )[/tex] and [tex]\left (x_{2},y_{2}\right )[/tex]
Since from the graph the two points closest to the line are[tex]\left ( 10,36 \right )[/tex] and [tex]\left ( 22,12 \right ).[/tex]
Equation of line with two points closest to the line :
[tex]y-y_{1}=m\cdot \left ( x-x_{1} \right )[/tex]
where m is the slope.
First we find the slope(m)=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{12-36}{22-10}[/tex]
on simplify we get, [tex]m=-2[/tex].
Now, to find the equation of the line: [tex]y-y_{1}=m\cdot \left ( x-x_{1} \right )[/tex]
[tex]y-36=\left ( -2 \right )\cdot \left ( x-10 \right )[/tex]
Apply distributive property on right hand side, we get
[tex]y-36=-2\cdot x+20[/tex]
Adding both sides by 36, we get
[tex]y=-2x+20+36[/tex]
[tex]y=-2x+56[/tex].
The equation for the linear model in the scatter plot obtained by the two closest point [tex]\left ( 10,36 \right ) and \left ( 22,12 \right )[/tex] closest to the line is,
[tex]y=-2x+56[/tex]
