Algebra 2: Find the equation

Question

Find the equation of a line passing through the point (-3, -7) that is perpendicular to the line 5x-3y=10. Show detailed steps.

Answer 1

a line perpendicular to 5x-3y =10 will have a negative inverse slope

-3y =-5x +10

y = 5x/3 - 10/3 has slope =5/3

the perpendicular lines all have slope = -3/5

take 5/3, change its sign and flip it upside down to get -3/5

through the given point (-3,-7)

is the line

y+7 = (-3/5)(x+3) in point slope form

or

5y+35=-3x-9

3x+5y = -44 in standard form

or

y = -3x/5 -44/5 in slope intercept form

or

3x+5y+44=0 in general form