To find the equation of the line passing through the points $(5, 1)$ and $(-1, 3)$, we will use the same steps as before.

1. Calculate the Slope $m$:

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting the points $(5, 1)$ and $(-1, 3)$:

$m = \frac{3 - 1}{-1 - 5} = \frac{2}{-6} = -\frac{1}{3}$

2. Write the Equation Using the Point-Slope Form:

Now, we'll use the point-slope form of the equation:

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

Using the slope $m = -\frac{1}{3}$ and one of the points, say $(5, 1)$:

$y - 1 = -\frac{1}{3}(x - 5)$

3. Convert to Slope-Intercept Form:

Now, expand and simplify to express the equation in slope-intercept form $y = mx + b$:

$y - 1 = -\frac{1}{3}x + \frac{5}{3}$

Add 1 to both sides:

$y = -\frac{1}{3}x + \frac{5}{3} + 1$

Convert 1 to a fraction with a denominator of 3:

$y = -\frac{1}{3}x + \frac{5}{3} + \frac{3}{3}$

Simplify:

$y = -\frac{1}{3}x + \frac{8}{3}$

So, the equation of the line is:

$y = -\frac{1}{3}x + \frac{8}{3}$

Would you like any more details or have any questions?

Here are 5 related questions:

1. How would you find the y-intercept from a given line equation?
2. How can you find the equation of a line perpendicular to this one?
3. What is the distance between the points $(5, 1)$ and $(-1, 3)$?
4. Can you write the equation of this line in standard form $Ax + By = C$?
5. How do you determine if a point lies on a given line?

Tip: When converting to slope-intercept form, simplify fractions carefully to ensure accuracy.