caroline is planting flowers in her garden. she plants her first 7 flowers in 4 minutes. after 12 minutes…

caroline is planting flowers in her garden. she plants her first 7 flowers in 4 minutes. after 12 minutes, she has planted 21 different flowers. which equation represents this direct variation?\na. $y = \\frac{4}{7}x$\nb. $y = \\frac{7}{4}x$\nc. $y = 4x + 7$\nd. $y = 7x$

caroline is planting flowers in her garden. she plants her first 7 flowers in 4 minutes. after 12 minutes, she has planted 21 different flowers. which equation represents this direct variation?\na. $y = \\frac{4}{7}x$\nb. $y = \\frac{7}{4}x$\nc. $y = 4x + 7$\nd. $y = 7x$

Answer

Explanation:

Step1: Recall direct - variation formula

The direct - variation formula is $y = kx$, where $k$ is the constant of variation. The constant of variation $k$ represents the rate.

Step2: Calculate the rate

Caroline plants 7 flowers in 4 minutes. The rate (constant of variation $k$) is the number of flowers planted per minute. So, $k=\frac{\text{Number of flowers}}{\text{Time}}=\frac{7}{4}$.

Step3: Write the direct - variation equation

Substituting $k = \frac{7}{4}$ into the direct - variation formula $y = kx$, we get $y=\frac{7}{4}x$.

Answer:

B. $y=\frac{7}{4}x$