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

`y=-(300)/(7)x+1000`

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)=(y_2-y_1)/(x_2-x_1)=(700-1000)/(7-0)=-(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=-(300)/(7)(x-0)`

`\implies y=-(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)=(y_2-y_1)/(x_2-x_1)=(710-940)/(7-1)=-(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=-(115)/(3)(x-1)`

`\implies y=-(115)/(3)x+(2935)/(3)`