Find the Line Through Points (2,2) and (9,16): Coordinate Geometry

To solve this problem, we'll calculate the slope of the line passing through the points $(2, 2)$ and $(9, 16)$.

• Step 1: Identify the coordinates
• Step 2: Apply the slope formula
• Step 3: Simplify the expression

Let's proceed:

Step 1: The coordinates given are $(x_1, y_1) = (2, 2)$ and $(x_2, y_2) = (9, 16)$.

Step 2: The slope $m$ of a line through two points is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the coordinates into the formula, we have:

$m = \frac{16 - 2}{9 - 2}$

Step 3: Simplify the expression:

$m = \frac{14}{7}$

$m = 2$

Therefore, the slope of the line is $\mathbf{m = 2}$.