Answer:
[tex]y=\frac{5}{6}x-2[/tex]
Step-by-step explanation:
Let the equation of a line passing through a point [tex](x_1,y_1)[/tex] and slope [tex]m_1[/tex] is,
[tex]y-y_1=m_1(x-x_1)[/tex]
Equation of the second line has been given as,
6x + 5y = 10
Slope-intercept form of the equation will be,
5y = -6x + 10
y = [tex]-\frac{6}{5}x+10[/tex]
Here slope of the line [tex]m_2=-\frac{6}{5}[/tex]
If both the lines are perpendicular,
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
[tex]m_1\times (-\frac{6}{5})=-1[/tex]
[tex]m_1=\frac{5}{6}[/tex]
Therefore, equation of the line passing through (6, 3) and slope = [tex]\frac{5}{6}[/tex] will be,
y - 3 = [tex]\frac{5}{6}(x-6)[/tex]
y = [tex]\frac{5}{6}x-5+3[/tex]
[tex]y=\frac{5}{6}x-2[/tex]
