What is an equation of the line that is perpendicular to 3x+y=−5 and passes through the point (3, −7) ?

y = x - 8

Step-by-step explanation:

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 3x + y = - 5 into this form

subtract 3x from both sides

y = - 3x - 5 ← in slope-intercept form

with slope m = - 3

given a line with slope m then the slope of a lin e perpendicular to it is

= - , hence

= - =

y = x + c ← is the partial equation

to find c substitute (3, - 7 ) into the partial equation

- 7 = 1 + c ⇒ c = - 7 - 1 = - 8

y = x - 8 ← equation of perpendicular line

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47