Answer:
Concept:
The formula to calculate the equation of a line is given below as
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]The coordinates given in the question are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(5,5) \\ (x_2,y_2)\Rightarrow(1,-1) \end{gathered}[/tex]By substituing the values in the formula above, we will have
[tex]\begin{gathered} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}} \\ \frac{-1-5}{1-5}=\frac{y-5}{x-5} \\ -\frac{6}{-4}=\frac{y-5}{x-5} \\ \frac{3}{2}=\frac{y-5}{x-5} \\ \end{gathered}[/tex]Cross multiply, we will have
[tex]\begin{gathered} \frac{3}{2}=\frac{y-5}{x-5} \\ 2(y-5)=3(x-5) \\ 2y-10=3x-15 \\ 2y=3x-15+10 \\ 2y=3x-5 \\ divide\text{ ball through by 2} \\ \frac{2y}{2}=\frac{3x}{2}-\frac{5}{2} \\ y=\frac{3}{2}x-\frac{5}{2} \end{gathered}[/tex]Hence,
The equation of the line is given below as
[tex]\Rightarrow y=\frac{3}{2}x-\frac{5}{2}[/tex]