Answer:
Equation of the line in the slope-intercept form will be [tex]y=-\frac{5}{3}x+20[/tex]
Step-by-step explanation:
An equation of the line perpendicular to [tex]y=\frac{3}{5}x+10[/tex] will be in the form of y = mx + c
Where m = slope of the line
c = y intercept of the line
From the property of the perpendicular line
[tex]m_{1}\times m_{2}=-1[/tex]
where [tex]m_{1}[/tex] and [tex]m_{2}[/tex] are the slopes of the perpendicular lines.
If [tex]m_{1}[/tex] = [tex]\frac{3}{5}[/tex]
then [tex]\frac{3}{5}\times m_{2}=-1[/tex]
[tex]m_{2}=-\frac{5}{3}[/tex]
So the equation will be [tex]y=-\frac{5}{3}x+c[/tex]
This line passes through the point (15, -5)
[tex](-5)=-\frac{5}{3}(15)+c[/tex]
-5 = -25 + c
c = 25 - 5
c = 20
Finally the equation will be [tex]y=-\frac{5}{3}x+20[/tex]
