#### Answer

$y - 4 = -\frac{5}{8}x - \frac{15}{8}$
$y = -\frac{5}{8}x + \frac{17}{8}$

#### Work Step by Step

We are given the two points $(5, -1)$ and $(-3, 4)$.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in the values into this formula:
$m = \frac{4 - (-1)}{-3 - 5}$
Subtract the numerator and denominator to simplify:
$m = -\frac{5}{8}$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$
Let's plug in the points and slope into the formula:
$y - 4 = -\frac{5}{8}(x - (-3))$
Use distribution to simplify:
$y - 4 = -\frac{5}{8}x - \frac{5}{8}(3)$
Multiply to simplify:
$y - 4 = -\frac{5}{8}x - \frac{15}{8}$
To change this equation into slope-intercept form, we need to isolate $y$. To isolate $y$, we add $4$ to each side of the equation:
$y = -\frac{5}{8}x - \frac{15}{8} + 4$
Change $4$ into an equivalent fraction that has $8$ as its denominator so that both fractions have the same denominator:
$y = -\frac{5}{8}x - \frac{15}{8} + \frac{32}{8}$
Add the fractions to simplify:
$y = -\frac{5}{8}x + \frac{17}{8}$
Now, we have the equation of the line in slope-intercept form.