Write the slope-intercept form of the equation of the line perpendicular to the graph of 4x-y=12 that passes through (8,2).

Question

Please explain the steps.

Answer 1

Hello, Christy

 

The first thing we must do is find the slope of 4x-y=12, and then find the negative reciprocal of that slope. Let's get started

4x-y=12            I am going to rewrite this as y=mx+b

-4x    -4x           Subtracting 4x... To isolate the variable y

-y= -4x+ 12      Divide both sides by -1

y= 4x-12           This is the slope-intercept form.. The slope

                         of this line is 4.  Its negative reciprocal is

                          (-1)/4

 

Remember, Christy, that if two lines are perpendicular their slopes are negative reciprocal of each other. That also means that when you multiply their respective slopes you get -1.  Since the slope of 4x-y=12 is 4, any line perpendicular to it must a slope of -1/4.. So, this is the slope that we need to use.

 

Ok, now we have the slope, -1/4, and we have a point, (8,2), where x1=8 and y1= 2. Let's use the point-slope form, and then rewrite the equation in the slope intercept form.  The point slope form is 

 

y-y1= m( x-x1)       Substituting -1/4 form, 8 for x1 and

y-2=(-1/4)(x-8)       2 for y.

y-2= (-1/4)x+2       Note: (-1/4)(-8)=2

  +2             +2

 Y= (-1/4)x+4         This is the slope intercept form

 

Well, glad to help.. Please rate my answer:)

 

D. Y. Taylor