Question

Suppose y varies directly with x. if y=-3 when x=5 find y when x=-1

Answer 1

Answer:

The value of y at x=-1 is 3/5.

Step-by-step explanation:

It is given that y varies directly with x. It means y is directly proportional to x.

$y\propto x$

$y=kx$              .... (1)

where, k is constant of proportionality.

It is given that y=-3 when x=5.

Substitute y=-3 and x=5 in equation (1).

$-3=k(5)$

$-\frac{3}{5}=k$

The value of k is -3/5.

$y=-\frac{3}{5}x$          .... (2)

We need to find the value of y when x=-1.

Substitute x=-1 in equation (2).

$y=-\frac{3}{5}(-1)$

$y=\frac{3}{5}$

Therefore the value of y at x=-1 is 3/5.

Answer 2

$\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x && y={{ k }}x \end{array} \\ \quad \\ \textit{we know that, when} \begin{cases} y=-3\\ x=5 \end{cases}\implies y=kx\implies (-3)=k(5)$

solve for "k", to find the "constant of variation",
then plug it back in the y = kx, to get the equation
now
what's is y when x = -1?
well, just plug that in the equation with the found "k" value,
to get "y" :)