Answer: [tex]\begin{gathered} Equation:\text{ }y\text{ = }\frac{5}{3}x \\ constant\text{ of variation = 5/3} \end{gathered}[/tex]
Explanation:
Given:
y varies directly as x
To find:
the equation relating y and x
find the constant of variation when x = -18/35, y = -6/7
We need to write the statement mathematically:
[tex]\begin{gathered} y\text{ }\propto\text{ x} \\ y\text{ = kx} \\ where\text{ k = constant of variation} \end{gathered}[/tex]
when x = -18/35, y = -6/7
[tex]\begin{gathered} \frac{-6}{7}\text{ = k\lparen}\frac{-18}{35}) \\ \\ \frac{-6}{7}\text{ = }\frac{-18k}{35} \\ cross\text{ multiply:} \\ -6(35)\text{ = -18k\lparen7\rparen} \\ -210\text{ = -126k} \end{gathered}[/tex][tex]\begin{gathered} divide\text{ both sides by -126:} \\ \frac{-210}{-126}\text{ = }\frac{-126k}{-126} \\ \\ k\text{ = 1.67 or 1}\frac{2}{3} \\ constant\text{ of variation is 1}\frac{2}{3} \end{gathered}[/tex]
The equation relating x and y:
[tex]y\text{ = }\frac{5}{3}x[/tex]
