Answer:
2x-5y=-49.
Explanation:
Given the line:
[tex]y=-\frac{5}{2}x-2[/tex]Comparing with the slope-intercept form: y=mx+b
[tex]\text{Slope,m}=-\frac{5}{2}[/tex]Two lines are perpendicular if the product of their slopes is -1.
Let the slope of the new line =n.
[tex]\begin{gathered} n\times-\frac{5}{2}=-1 \\ n=\frac{2}{5} \end{gathered}[/tex]Therefore, the equation of the perpendicular line passing through (-7,7) is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-7=\frac{2}{5}(x-(-7)) \\ y-7=\frac{2}{5}(x+7) \\ 5(y-7)=2(x+7) \\ 5y-35=2x+14 \\ 2x-5y=-35-14 \\ 2x-5y=-49 \end{gathered}[/tex]The equation of the line is 2x-5y=-49.
