Question

write the slope intercept equation for the line that passes through (-5,-8) and is perpendicular to 10x-6y=-11

Answer 1

slope intercept form of an equation of a line is of the form
y=mx + b

m is the sope
b is the intercept

first write the equation of the given line in its sope intercept form
i.e 10x-6y=-11
is the same as
\[y=\frac{ 10 }{ 6x }+ \frac{ 11 }{ 10 }\]
from the equation notice the slope of the given line is 10/6 or 5/3.
and two lines are perpendicular to one another if the slope of one line is the negative reciprocal to the other
so the equation of the perpendicular line is -3/5.
the equation of the line perpendicular to 10x - 6y=-11 and passing through (-5,-8) can be found using the point slope form of equation of a
line(y-y1=m(x-x1)
so we know the slope and the pt it passes through
m=-3/5
pt.(-5,-8)

y-(-8)=-3/5(x-(-5))
y+8=-3/5x-3
but this is just the point slope form the required is in slope intercept which is
y=-3/5x-3-8
y=-3/5x-11 is your answer