Answer:
The y-intercept of the equation of the line is 20.
Step-by-step explanation:
The equation of given line is
[tex]y=\frac{3}{5}x+10[/tex]
It is a slope intercept form of a line (y=mx+b), where m is slope and b is y-intercept.
The slope of the line is
[tex]m_1=\frac{3}{5}[/tex]
The product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]\frac{3}{5}\times m_2=-1[/tex]
[tex]m_2=-\frac{5}{3}[/tex]
The slope of required line is [tex]-\frac{5}{3}[/tex] and it is passing through the point (15,-5).
The point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-5)=-\frac{5}{3}(x-15)[/tex]
[tex]y+5=-\frac{5}{3}(x)+25[/tex]
[tex]y=-\frac{5}{3}(x)+20[/tex]
The slope intercept form of required line is [tex]y=-\frac{5}{3}(x)+20[/tex].
Therefore y-intercept of line is 20.
