Question

which of the following equations represents the line that passes through the points (2, -6) and (-4, 3)?
\\( y = -\frac{2}{3}x - 3 \\)
\\( y = -\frac{3}{2}x - 3 \\)
\\( y = -\frac{3}{2}x - 7 \\)
\\( y = -\frac{2}{3}x + \frac{1}{3} \\)

Explanation:

Step1: Calculate slope

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-6)}{-4 - 2} = \frac{9}{-6} = -\frac{3}{2}$

Step2: Find y-intercept b

Use point $(2, -6)$: $-6 = -\frac{3}{2}(2) + b$
Simplify: $-6 = -3 + b$, so $b = -3$

Step3: Write line equation

$y = -\frac{3}{2}x - 3$

Answer:

$y = -\frac{3}{2}x - 3$