We are given the following information
Slope of the line = m = -3
The line passes through the point (5, -7)
Recall that the equation of a line in the point-slope form is given by
[tex](y-y_1)=m(x_{}-x_1)[/tex]Where m is the slope and (x₁, y₁) is a point on the line.
Let us substitute the given values into the above equation
[tex]\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=-3x+8[/tex]