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