Respuesta :
The line is perpendicular to the equation:
[tex]y=3x+5[/tex]So our slope will be the negative reciprocal of the slope of this line so the new slope will be:
[tex]m=-\frac{1}{3}[/tex]Now with the slope we can find the intercept in the y axis with the slope equation:
[tex]m=\frac{y-y_1}{x-x_1}[/tex]So we replace the slope and the coordinate, and replace x=0 to find the intercept so:
[tex]\begin{gathered} -\frac{1}{3}=\frac{y-4}{0-(-1)} \\ y-4=-\frac{1}{3} \\ y=4-\frac{1}{3} \\ y=\frac{11}{3} \end{gathered}[/tex]So the general equation will be:
[tex]y=-\frac{1}{3}x+\frac{11}{3}[/tex]