Question

The equation of a function is y= -1/3 x -2/5. Find

a) the value of y when x=4

b) the value of x when y= -2/3

Answer 1

Given equation :

$\tt \implies y = - \dfrac{1}{3}x - \frac{2}{5}$

To Find :

1. Value of y when x=4
2. Value of x when y= -2/3

Solution :

Case 1

$\tt \implies y = - \dfrac{1}{3} \times 4 - \frac{2}{5} \\ \\ \tt \implies y = - \dfrac{4}{3} - \frac{2}{5} \\ \\ \tt \implies y = \frac{ - 20 - 6}{15} \\ \\ \implies \boxed{ \tt y = \frac{ - 26}{15}}$

Case 2

$\tt \implies y = - \dfrac{1}{3}x - \frac{2}{5} \\ \\ \tt \implies - \frac{2}{3} = - \frac{1}{3} x - \frac{2}{5} \\ \\\tt \implies -\frac{1}{3}x = - \frac{ 2}{3} + \frac{2}{5} \\ \\\tt \implies -\frac{1}{3}x = \frac{ - 10 + 6}{15} \\ \\ \tt \implies -\frac{1}{3}x = \frac{ - 4}{15} \\ \\\tt \implies x = \frac{ - 4}{15} \times (-3) \\ \\\tt \implies x = \frac{12}{15} \\ \\ \large \implies \boxed{ \tt x = \frac{4}{5} }$

Answer 2

Given equation,

$y = \dfrac{-1}{3} x - \dfrac{2}{5}$

a) When x = 4

$\implies y = \dfrac{-1}{3} (4) - \dfrac{2}{5}$

$\implies y = \dfrac{-4}{3}-\dfrac{2}{5}$

$\implies y = \dfrac{-20-6}{15}$

$\implies \boxed{\boxed{\bold{y = \dfrac{-26}{15} }}}}}$

b) When y = -2/3

$\implies \dfrac{-2}{3} = \dfrac{-1}{3}x-\dfrac{2}{5}$

$\implies \dfrac{-1}{3}x=\dfrac{-2}{3}+\dfrac{2}{5}$

$\implies \dfrac{-1}{3}x=\dfrac{-10+6}{15}$

$\implies \dfrac{-1}{3}x=\dfrac{-4}{15}$

$\implies x = \dfrac{-4}{15} * \dfrac{3}{-1}$

$\implies \boxed{\boxed{\bold{ x = \frac{4}{5} }}}}}}$