Respuesta :
Answer:
[tex]y=-\frac{x}{3}-\frac{11}{3}[/tex]Explanation:
The point-slope form of the equation of a line is given as;
[tex]y-y_1=m(x-x_1)[/tex]where m = the slope of the line
x1 and y1 = coordinates of a point on the line
Given the coordinates (1,-4) and (-5,-2), let's go ahead and determine the slope of the line where x1 = 1, y1 = -4, x2 = -5 and y2 = -2;
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-4)}{-5-1}=\frac{-2+4}{-6}=-\frac{2}{6}=-\frac{1}{3}[/tex]Since our m = -1/3, let's go ahead and write the required equation using the point (1, -4) where x1 = 1 and y1 = -4;
[tex]\begin{gathered} y-(-4)=-\frac{1}{3}(x-1) \\ y+4=-\frac{x}{3}+\frac{1}{3} \\ y=-\frac{x}{3}+\frac{1}{3}-4 \\ y=-\frac{x}{3}-\frac{11}{3} \end{gathered}[/tex]