Answer:
y = (-5/6)x + 4
Explanation:
The equation of a line can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]Where (x1, y1) is one point in the line and m is the slope and can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x2, y2) is another point in the line.
So, replacing (x1, y1) by (-12, 14) and (x2, y2) by (6, -1), we get that the slope is equal to:
[tex]m=\frac{-1-14}{6-(-12)}=\frac{-15}{6+12}=\frac{-15}{18}=-\frac{5}{6}[/tex]Then, with a slope equal to -5/6 and the point (-12, 14), we get that the equation of the line is:
[tex]\begin{gathered} y-14=-\frac{5}{6}(x-(-12)) \\ y-14=-\frac{5}{6}(x+12) \end{gathered}[/tex]So, solving for y, we get:
[tex]\begin{gathered} y-14=-\frac{5}{6}\cdot x-\frac{5}{6}\cdot12 \\ y-14=-\frac{5}{6}x-10 \\ y=-\frac{5}{6}x-10+14 \\ y=-\frac{5}{6}x+4 \end{gathered}[/tex]Therefore, the answer is y = (-5/6)x + 4