Find the Line Through Points (3,7) and (6,14): Coordinate Geometry

To solve this problem, we'll calculate the slope of the line passing through the points $(3, 7)$ and $(6, 14)$. The formula for the slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

• $m = \frac{y_2 - y_1}{x_2 - x_1}$

First, we identify our points as follows:
Point 1: $(x_1, y_1) = (3, 7)$
Point 2: $(x_2, y_2) = (6, 14)$

Next, apply the formula:
$x_1 = 3 \\ y_1 = 7 \\ x_2 = 6 \\ y_2 = 14 \\$
Substitute into the slope formula:
$m = \frac{14 - 7}{6 - 3} = \frac{7}{3}$

Therefore, the slope of the line is $m = \frac{7}{3} = 2\frac{1}{3}$.

The correct choice from the given options is: $m=2\frac{1}{3}$.