Answer:
Equation of line in slope-intercept form:
[tex]y=-\frac{6}{5}x+\frac{7}{5}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is:
y = mx + c
where m is the slope and c is the y-intercept.
Given that (-3,5) passes through the line,hence:
5 = -3m+c ------------1
Also the line is perpendicular to 5x - 6y = 9.
Slope of a line ax+by+c=0 is [tex]\frac{-a}{b}[/tex]
Hence slope of 5x - 6y = 9 is [tex]\frac{5}{6}[/tex]
Relation between slopes of two perpendicular lines:
[tex]m_1\times m_2=-1[/tex]
Using above relation, m= [tex]-\frac{6}{5}[/tex].
Substituting m = -6/5 in equation 1, we get:
c = 5 + 3(-6/5)
[tex]c=\frac{7}{5}[/tex]
Putting m = [tex]-\frac{6}{5}[/tex] and c = [tex]\frac{7}{5}[/tex]
we get:
[tex]y=-\frac{6}{5}x+\frac{7}{5}\\6x+5y=7[/tex]
