Write the equation of a line perpendicular to -2y = 8 + 6x and passsing through the point (-1,5)

Question

need help solving this question

Answer 1

-2y = 8 + 6x

first we convert this equation in slope intercept form

 y = -3x -4

 

slope of this line is -3

 

so slope of perpendicular line  is 1/3 -----(If two lines are perpendicular, their slopes are negative reciprocals)

 

It passsing through the point (-1,5)

 

y = mx + b

 

we will substitute vale of (x,y) =(-1,5)

 

5=1/3(-1) + b

 

5=-1/3 +b

 

5+ 1/3 = b

 

16/3 = b

 

so equation f line is

 y= (1/3)x + 16/3

 

Answer 2

-2y = 8 + 6x      Solve for y

y = -3x - 4      The slope of this line is -3. Perpendicular lines have slopes that are negative reciprocals of each other.

So, the slope of the new line will be 1/3.

Now, use the point slope form for the equation of a line: y-y₁ = m(x-x₁)

y-5 = 1/3(x+1)

y-5 = (1/3) x + 1/3

y = (1/3)x + 5 1/3