Find an equation of the line. Write the equation using function notation.
-$\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)$
A) $y = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$
B) $y = 9 x - \frac { 77 } { 9 }$
C) $f(x) = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$
D) f(x)=9x-3

Question

Quizplus · Accepted Answer

To find the equation of the line, we first calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, we get $m = \frac{\frac{4}{3} - \frac{4}{9}}{9 - 1} = \frac{\frac{8}{9}}{8} = \frac{1}{9}$. Then, using the point-slope form $y - y_1 = m(x - x_1)$ with one of the given points, we find the equation of the line. Substituting $m = \frac{1}{9}$ and the point $(1, \frac{4}{9})$, we get $y - \frac{4}{9} = \frac{1}{9}(x - 1)$. Simplifying, we find $y = \frac{1}{9}x + \frac{1}{3}$, which, when written in function notation, is $f(x) = \frac{1}{9}x + \frac{1}{3}$.

Find an Equation of the Line (1,49),(9,43)\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)(1,94​),(9,34​)

Find an Equation of the Line $\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)$