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The eqaution of a line between two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging our points we have:
[tex]\begin{gathered} y-(-7)=\frac{-1-(-7)}{2-4}(x-4) \\ y+7=\frac{6}{-2}(x-4) \\ y+7=-3(x-4) \\ y+7=-3x+12 \\ y=-3x+12-7 \\ y=-3x+5 \end{gathered}[/tex]Therefore the equation is:
[tex]y=-3x+5[/tex]