Question

suppose that y varies directly with x, and y = 9 when x = 3. (a) write a direct variation equation that relates x and y. equation: (b) find y when x = -7. y =

Explanation:

Step1: Recall direct variation form

Direct variation follows $y = kx$, where $k$ is the constant of variation.

Step2: Solve for $k$ using given values

Substitute $y=9$, $x=3$:
$$9 = k(3)$$
$$k = \frac{9}{3} = 3$$

Step3: Write the variation equation

Substitute $k=3$ into $y=kx$:
$y = 3x$

Step4: Find $y$ when $x=-7$

Substitute $x=-7$ into $y=3x$:
$$y = 3(-7) = -21$$

Answer:

(a) $y = 3x$
(b) $y = -21$