Find the Line Equation Through Points (15,36) and (5,16): Two-Point Form

Let's solve the problem to find the equation of the line.

To determine the equation of the line, we first need to calculate the slope $m$ of the line passing through the points $(15, 36)$ and $(5, 16)$. The formula for the slope is given by:

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

Substituting the given points into the formula:

$m = \frac{16 - 36}{5 - 15} = \frac{-20}{-10} = 2$

Thus, the slope $m$ is 2.

With the slope and one of the points, we can use the point-slope form of the line equation:

$y - y_1 = m(x - x_1)$

We'll use the point $(5, 16)$:

$y - 16 = 2(x - 5)$

Expanding the equation, we get:

$y - 16 = 2x - 10$

Add 16 to both sides to solve for $y$:

$y = 2x - 10 + 16$

$y = 2x + 6$

Therefore, the equation of the line is $y = 2x + 6$.