Answer:
[tex]y=-\frac{2}{5}x+1[/tex]Step-by-step explanation:
The equation of a line is represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}[/tex]If the given line is perpendicular to the one we want to find, the slope of the missing line would be the negative reciprocal of the given slope:
[tex]\begin{gathered} m=-(\frac{2}{5}) \\ m=-\frac{2}{5} \end{gathered}[/tex]Use the slope-point form of the line equation to determine the equation in slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=-\frac{2}{5}(x-5) \\ y+1=-\frac{2}{5}x+2 \\ y=-\frac{2}{5}x+2-1 \\ y=-\frac{2}{5}x+1 \end{gathered}[/tex]