5x + 3y = - 53
the equation of a line in ' slope- intercept form ' is y = mx + c
where m is the slope and c the y-intercept
rearrange 3x - 5y = - 15 into this form to obtain m → (subtract 3x from both sides)
- 5y = - 3x - 15 → divide all terms by - 5 )
y =
x + 3 → in slope-intercept form with m = 
given a line with slope m then the slope m₁ of a line perpendicular to it is
m₁ = -
= - 1 ÷
= - 
partial equation is y = -
x + c
to find c substitute ( - 7, - 6) into the partial equation
- 6 =
+ c ⇒ c = - 6 -
= - 
y = -
x -
→ in slope intercept form
multiply all terms by 3
3y = - 5x - 53 → ( add 5x to both sides )
5x + 3y = - 53 → in standard form