Question

if y varies directly as x and y=49 when x=7, what is the value of y when x=3?
a. 7
b. 9
c. 49
d. 21

Answer 1

\(\large\color{black}{ \displaystyle y=\color{orangered}{\rm k} x}\)
this above, is the equation of a direct variation.

In this equation x and y are directly proportional to y, so that you can multiply x by some constant k and obtain y. (this perfect proportion is called direct variation)

it is a line with a slope k that goes through the origin.

Answer 2

If you are given that that `y=49 when x=7` then you can go ahead and find the constant k.

plug in 49 for y and 7 for k, into the \(\large\color{black}{ \displaystyle y=\color{orangered}{\rm k} x}\)

Answer 3

and then after plugging in solve for k

Answer 4

When you find the k,
you can figure out the value of y when x=3.

How? you can plug in the value of k you just found, and plug 3 instead of x.
(again u r plugging into \(\large\color{black}{ \displaystyle y=\color{orangered}{\rm k} x}\) )