Answer:
x-y=-6
Explanation:
Given the points (-1,5) and (-5,1):
To find the equation of the line, we use the two-point formula:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=(-1,5) \\ \mleft(x_2,y_2\mright)=\mleft(-5,1\mright?) \end{gathered}[/tex]Substitute these points into the formula:
[tex]\frac{y-5}{x-(-1)}=\frac{1-5}{-5_{}-(-1)}[/tex]Then simplify:
[tex]\begin{gathered} \frac{y-5}{x+1}=\frac{1-5}{-5_{}+1} \\ \frac{y-5}{x+1}=\frac{-4}{-4} \\ \frac{y-5}{x+1}=1 \\ y-5=x+1 \\ -5-1=x-y \\ x-y=-6 \end{gathered}[/tex]The equation of the line is:
[tex]x-y=-6[/tex]