Question

find an equation for the line below.

Explanation:

Identify points on the line

$$ (x_1, y_1) = (-6, 5) $$

$$ (x_2, y_2) = (2, -5) $$

Calculate the slope

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 5}{2 - (-6)} = \frac{-10}{8} = -\frac{5}{4} $$

Determine the equation of the line

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

$$ y - 5 = -\frac{5}{4}(x + 6) $$

$$ y = -\frac{5}{4}x - \frac{15}{2} + 5 $$

$$ y = -\frac{5}{4}x - \frac{5}{2} $$

Answer:

\(y = -\frac{5}{4}x - \frac{5}{2}\)