Answer:
[tex]\displaystyle (y - 2) = -\frac{2}{3}\, (x + 8)[/tex].
Step-by-step explanation:
Given two points [tex](x_0,\, y_0)[/tex] and [tex](x_1,\, y_1)[/tex] on a line in [tex]\mathsf{2D}[/tex], the slope of that line would be:
[tex]\begin{aligned} m &= \frac{y_1 - y_0}{x_1 - x_0} \\ &= \frac{-4 - 2}{1 - (-8)} = -\frac{2}{3}\end{aligned}[/tex].
For a line with slope [tex]m[/tex] and a point [tex](x_0,\, y_0)[/tex], the point-slope equation of that line would be:
[tex]y - y_0 = m \, (x - x_0)[/tex].
It was already found that for this line, slope [tex]\displaystyle m = -\frac{2}{3}[/tex]. Take [tex](x_0,\, y_0) = (-8,\, 2)[/tex]. That is: [tex]x_0 = -8[/tex] and [tex]y_0 = 2[/tex]. Find the equation of this line in point-slope form:
[tex]\displaystyle (y - \underbrace{2}_{y_0}) = \underbrace{\left(-\frac{2}{3}\right)}_{m}\, (x - \underbrace{(-8)}_{x_0})[/tex].
Equivalently:
[tex]\displaystyle (y - 2) = -\frac{2}{3}\, (x + 8)[/tex].
