Question

Calculate the line of best fit using m= y2-y1/x2-x1 using your brain not a calculator

Answer 1

Take two points

• (1,940)
• (2,950)

Slope

• m=950-940/2-1=10

Equation in point slope form

• y-y1=m(x-x1)
• y-940=10(x-1)
• y-940=10x-10
• y=10x-10+940
• y=10x+930

Answer 2

Answer:

$y=-\dfrac{300}{7}x+1000$

Step-by-step explanation:

Method 1  (see attachment 1 with red line)

Plots the points on a graph and draw a line of best fit, remembering to ensure the same number of points are above and below the line.

Use the two end-points of the line of best fit to find the slope:

$\textsf{let}\:(x_1,y_1)=(0,1000)$

$\textsf{let}\:(x_2,y_2)=(7,700)$

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{700-1000}{7-0}=-\dfrac{300}{7}$

Input the found slope and point (0, 1000) into point-slope form of a linear equation to determine the equation of the line of best fit:

$\implies y-y_1=m(x-x_1)$

$\implies y-1000=-\dfrac{300}{7}(x-0)$

$\implies y=-\dfrac{300}{7}x+1000$

Method 2  (see attachment 2 with blue line)

If you aren't able to plot the points, you should be able to see that the general trend is that as x increases, y decreases.  Therefore, take the first and last points in the table and use these to find the slope:

$\textsf{let}\:(x_1,y_1)=(1,940)$

$\textsf{let}\:(x_2,y_2)=(7,710)$

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{710-940}{7-1}=-\dfrac{115}{3}$

Input the found slope and point (1, 940) into point-slope form of a linear equation to determine the equation of the line of best fit:

$\implies y-y_1=m(x-x_1)$

$\implies y-940=-\dfrac{115}{3}(x-1)$

$\implies y=-\dfrac{115}{3}x+\dfrac{2935}{3}$