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

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 point $(2,7)$ in each equation

For $y = 4x−1$, when $x = 2$, $y=4\times2 - 1=8 - 1 = 7$, but it is not in the form $y = kx$ (it has a non - zero constant term), so it's not a direct variation. For $y=\frac{7}{x}$, it is an inverse variation ($y=\frac{k}{x}$ form), 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 $x = 2$, $y=\frac{7}{2}\times2 = 7$, and it is in the form $y = kx$ with $k=\frac{7}{2}$.

Answer:

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