which relation is a direct variation that contains the ordered pair (2, 7)?\n○ y = 4x - 1\n○ y =…

Explanation:

Step1: Recall direct - variation form

The form of a direct - variation equation is $y = kx$, where $k$ is the constant of variation.

Step2: Test the ordered pair $(2,7)$ in each option

For $y = 4x-1$, when $x = 2$, $y=4\times2 - 1=8 - 1=7$, but it is not in the form $y = kx$ (it is a linear non - direct variation). For $y=\frac{7}{x}$, it is an inverse variation, not a direct variation. For $y=\frac{2}{7}x$, when $x = 2$, $y=\frac{2}{7}\times2=\frac{4}{7}\neq7$. For $y=\frac{7}{2}x$, when $x = 2$, $y=\frac{7}{2}\times2 = 7$.

Answer:

$y=\frac{7}{2}x$