Answer:
The equation of the line of best fit is y = x + 2
Step-by-step explanation:
To find the equation of the line of best fit chose two points when the line passing through them the number of points over it equals the number of point below it
- The form of the equation is y = m x + b, where m is the slope of the line and b is the y-intercept (y at x = 0)
- The formula of the slope is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
From the attached graph the points (37 , 39) and (47 , 49) are the best choice to make the equation of the line of best fit
∵ The line passes through points (37 , 39) and (47 , 49)
∴ [tex]x_{1}[/tex] = 37 and [tex]x_{2}[/tex] = 47
∴ [tex]y_{1}[/tex] = 39 and [tex]y_{2}[/tex] = 49
- Substitute them in the formula of the slope
∵ [tex]m=\frac{49-39}{47-37}=\frac{10}{10}[/tex]
∴ m = 1
- Substitute the value of m in the form of the equation
∴ y = (1) x + b
∴ y = x + b
- To find b substitute x and y in the equation by the coordinates
of one of the two points above
∵ x = 37 and y = 39
∴ 39 = 37 + b
- Subtract 37 from both sides
∴ 2 = b
∴ y = x + 2
The equation of the line of best fit is y = x + 2
