Question

find an equation for the line that passes through the points $(-4, 1)$ and $(2, -3)$.

Explanation:

Step1: Calculate slope of the line

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substitute $(x_1,y_1)=(-4,1)$ and $(x_2,y_2)=(2,-3)$:
$m = \frac{-3 - 1}{2 - (-4)} = \frac{-4}{6} = -\frac{2}{3}$

Step2: Use point-slope form

Point-slope form: $y - y_1 = m(x - x_1)$. Use $(x_1,y_1)=(-4,1)$:
$y - 1 = -\frac{2}{3}(x - (-4))$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 1 = -\frac{2}{3}x - \frac{8}{3}$
$y = -\frac{2}{3}x - \frac{8}{3} + 1$
$y = -\frac{2}{3}x - \frac{5}{3}$

Step4: Convert to standard form (optional)

Multiply all terms by 3 to eliminate fractions:
$3y = -2x - 5$
$2x + 3y = -5$

Answer:

$y = -\frac{2}{3}x - \frac{5}{3}$ (or $2x + 3y = -5$)