## Algebra 1: Common Core (15th Edition)

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