Question

What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?

Answer 1

The best choice would probably be C. We know the y-intercept is higher than 46 and that the slope is negative. That leaves us with choice A and C. We can eliminate A because when using the slope formula, the answer is closer to 2 than 3. However, even though it's most likely C, I would check first.

Answer 2

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 $\left (x_{1},y_{1} \right )$ and $\left (x_{2},y_{2}\right )$

Since from the graph the two points closest to the line are$\left ( 10,36 \right )$ and $\left ( 22,12 \right ).$

Equation of line with two points closest to the line :

                                                    $y-y_{1}=m\cdot \left ( x-x_{1} \right )$

where m is the slope.

First we find the slope(m)=$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$  

$m=\frac{12-36}{22-10}$

on simplify we get,  $m=-2$.

Now, to find  the equation of the line:  $y-y_{1}=m\cdot \left ( x-x_{1} \right )$

$y-36=\left ( -2 \right )\cdot \left ( x-10 \right )$

Apply distributive property on right hand side, we get

$y-36=-2\cdot x+20$

Adding both sides by 36, we get

$y=-2x+20+36$

$y=-2x+56$.

The equation for the linear  model in the scatter plot obtained by the two closest point $\left ( 10,36 \right ) and \left ( 22,12 \right )$ closest to the line is,

$y=-2x+56$