Question

suppose that y varies directly with x, and y = 15 when x = 6.
(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 is $y = kx$, where $k$ is the constant of variation.

Step2: Solve for $k$ using given values

Substitute $y=15$, $x=6$:
$$15 = k \times 6$$
$$k = \frac{15}{6} = \frac{5}{2}$$

Step3: Write the direct variation equation

Substitute $k=\frac{5}{2}$ into $y=kx$:
$$y = \frac{5}{2}x$$

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

Substitute $x=7$ into the equation:
$$y = \frac{5}{2} \times 7 = \frac{35}{2}$$

Answer:

(a) $y = \frac{5}{2}x$
(b) $y = \frac{35}{2}$