y = - x - 1
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
rearrange - 7x + 5y = 12 into this form
add 7x to both sides
5y = 7x + 12 ( divide all terms by 5 )
y = x +
← in slope- intercept form
with slope m =
given a line with slope m then the slope of a line perpendicular to it is
perpendicular slope = - = -
The partial equation of the perpendicular line is
y = - x + c
to find c substitute (- 7, 4 ) into the partial equation
4 = 5 + c ⇒ c = 4 - 5 = - 1
y = - x - 1 ← in slope- intercept form