If y varies directly as x, find a linear function which relates them.
-$$y = 3 \text { when } x = \frac { 1 } { 4 }$$
A) $f ( x ) = x + \frac { 11 } { 4 }$
B) $f ( x ) = \frac { x } { 3 }$
C) $f ( x ) = 12 x$
D) $f ( x ) = \frac { x } { 12 }$

Question

If y varies directly as x, find a linear function which relates them.
-$$y = 3 \text { when } x = \frac { 1 } { 4 }$$ 
A) $f ( x ) = x + \frac { 11 } { 4 }$
B) $f ( x ) = \frac { x } { 3 }$
C) $f ( x ) = 12 x$
D) $f ( x ) = \frac { x } { 12 }$

Quizplus · Accepted Answer

Since $y$ varies directly as $x$, the relationship can be expressed as $y = kx$, where $k$ is the constant of variation. Given $y = 3$ when $x = \frac{1}{4}$, we can find $k$ by substituting these values into the equation: $3 = k \cdot \frac{1}{4}$, which gives $k = 12$. Therefore, the linear function that relates $y$ and $x$ is $y = 12x$, which corresponds to option C.

If Y Varies Directly as X, Find a Linear Function y=3 when x=14y = 3 \text { when } x = \frac { 1 } { 4 }y=3 when x=41​

If Y Varies Directly as X, Find a Linear Function $y = 3 \text { when } x = \frac { 1 } { 4 }$