Algebra 1: Common Core (15th Edition)

$y = -\frac{1}{3}x + 4$
We are given the points $(-6, 6)$ and the point $(3, 3)$. 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: $m = \frac{3 - 6}{3 - (-6)}$ Subtract the numerator and denominator to simplify: $m = \frac{-3}{9}$ To simplify, divide the numerator and denominator by their greatest common factor, $3$: $m = -\frac{1}{3}$ 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: $y - 3 = -\frac{1}{3}(x - 3)$ Use distribution to simplify: $y - 3 = -\frac{1}{3}x - (-\frac{3}{3})$ Simplify the fraction by dividing by their greatest common factor, $3$: $y - 3 = -\frac{1}{3}x + 1$ To change this equation into point-intercept form, we need to isolate $y$. To isolate $y$, we add $3$ to each side of the equation: $y = -\frac{1}{3}x + 1 + 3$ Add constants to simplify: $y = -\frac{1}{3}x + 4$ Now, we have the equation of the line in slope-intercept form.