Given :
We have the points: (-6, 2), (4, -4)
The equation of a line given two points can be found using the formula:
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting we have:
[tex]\begin{gathered} \frac{y\text{ - }2}{x-(-6)}\text{ = }\frac{-4-2}{4-(-6)} \\ \frac{y-2}{x+6}=\frac{-6}{10} \\ \text{Cross}-\text{Multiply} \\ 10(y-2)\text{ = -6(x + 6)} \\ 10y\text{ - 20 = -6x - 36} \\ \text{Collect like terms} \\ 10y\text{ = -6x - 36 + 20} \\ 10y\text{ = -6x - 16} \end{gathered}[/tex]Answer: 10y = -6x - 16
