The equation of the line that fit the data is 2 x + 3 y = 398
Step-by-step explanation:
To find the equation of a line from two points on the line use this form
[tex]\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where
∵ A line passes through points (64 , 90) and (97 , 68)
∴ [tex]x_{1}[/tex] = 64 and [tex]y_{1}[/tex] = 90
∴ [tex]x_{2}[/tex] = 97 and [tex]y_{2}[/tex] = 68
- Substitute these values in the rule above
∴ [tex]\frac{y-90}{x-64}=\frac{68-90}{97-64}[/tex]
∴ [tex]\frac{y-90}{x-64}=\frac{-22}{33}[/tex]
∴ [tex]\frac{y-90}{x-64}=\frac{-2}{3}[/tex]
- By using cross multiplication
∴ 3(y - 90) = -2(x - 64)
- Simplify
∵ 3(y) - 3(90) = (-2)(x) - (-2)(64)
∴ 3 y - 270 = -2 x + 128
- Add 2 x for both sides
∴ 2 x + 3 y - 270 = 128
- Add 270 to both sides
∴ 2 x + 3 y = 398
The equation of the line that fit the data is 2 x + 3 y = 398
Learn more:
You can learn more about linear equation in brainly.com/question/12363217
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