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Vsevolod [243]
2 years ago
11

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

Mathematics
2 answers:
jeka942 years ago
8 0

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
hodyreva [135]2 years ago
5 0

Answer:

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

Step-by-step explanation:

<u>Method 1</u>  (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

<u>Method 2</u>  (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}

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