Question

What is the equation of a line that passes through the point (-3,7) and is perpendicular to the line 2y+6x=12

Answer 1

What is the equation of a line that passes through the point (-3,7) and is perpendicular to the line 2y+6x=12​

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

so

The given line is

2y+6x=12

step 1

Find the slope

isolate the variable y

2y=-6x+12

y=-3x+6

the slope is m=-3

therefore

the slope of teh perpendicular line is

m=1/3

step 2

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=1/3

(x1,y1)=(-3,7)

substitute

y-7=(1/3)(x+3)

convert to slope intercept form

isolate the variable y

y-7=(1/3)x+1

y=(1/3)x+8