MATH SOLVE

2 months ago

Q:
# The data plots ((64,90) and (97,68) seem to be on a line that “fits” the data. Write an equation

Accepted Solution

A:

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[tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points on the line(x , y) are the coordinates of any general point on the line∵ 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#LearnwithBrainly