Find the Line Through Points (5,7) and (1,3): Coordinate Geometry

To solve this problem, we'll follow these steps:

• Identify the coordinates of the points.

• Apply the slope formula.

• Calculate the slope value.

Let's work through the steps:

We are given two points on a line: $(5,7)$ and $(1,3)$.

Step 1: Assign the coordinates: $(x_1, y_1) = (5, 7)$ and $(x_2, y_2) = (1, 3)$.

Step 2: Use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Substitute the coordinates into the formula:
$m = \frac{3 - 7}{1 - 5} \\ = \frac{-4}{-4} \\ = 1$

Therefore, the slope of the line passing through the points $(5,7)$ and $(1,3)$ is $\bm{m = 1}$.

Thus, the correct answer is $\bm{m = 1}$, corresponding to choice 1.