Given:
y varies directly with x,
It is given that y = 7 when x = -9.
To find:
The value of y when x = 27 for the direct variation.
Solution:
It is given that y varies directly with x, so
[tex]y\propto x[/tex]
[tex]y=kx[/tex] ...(i)
Where, k is the constant of proportionality.
It is given that y = 7 when x = -9. Putting these values in (i), we get
[tex]7=k(-9)[/tex]
[tex]-\dfrac{7}{9}=k[/tex]
Putting [tex]k=-\dfrac{7}{9}[/tex] in (i), we get
[tex]y=-\dfrac{7}{9}x[/tex]
Putting [tex]x=27[/tex], we get
[tex]y=-\dfrac{7}{9}(27)[/tex]
[tex]y=-21[/tex]
Therefore, the required value is [tex]y=-21[/tex].
