To calculate the equation of a line passing through two points, we use the formula;
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where (x}_1,y_1)=(4,5)and(x_2,y_2)\text{ = (8, -3)} \\ \text{Putting these values in the formula we have;} \\ \frac{y-5}{x-4}=\frac{-3-5}{8-4} \\ \frac{y-5}{x-4}=\frac{-8}{2} \\ \frac{y-5}{x-4}=\frac{-4}{1} \end{gathered}[/tex][tex]\begin{gathered} \text{Cross multiplying, we have} \\ y-5=\text{ -4(x-4)} \\ y-5=-4x+16 \\ y=-4x+16+5 \\ y=-4x+21 \end{gathered}[/tex]Therefore the equation of the line is y = -4x + 21
