Find an equation of the line. Write the equation using function notation. Through (5,-3); perpendicular to 4y =x-8

Question

i need help solving this problem

Answer 1

First of all, you are given a line  written as such:  4Y= X-8.    You need to slove for "y" because you need to find the

 

slope of this line to determine what a perpendicular slope would be. 

 

1.  Divide both sides of the equation by the number next to "Y."      Y= (X -8)/4  = x/4 -8/4     Y= 1/4 X  -2

 

2.  Therefore, its slope is the number next to "X."     m= 1/4  = slope.

 

3.  Next we are told that we are to write an equation  that is perpendicular to the equation 4y= X -8.

 

    This equation's slope is 1/4, but a line perpendicular to it would be the negative reciprocal.  In other  words, change 1/4 to 4/1  and make it negative, so it becomes  -4/1.  The perpendicular line must have a slope of -4/1.

 

4.  Use the point-slope form to find your equation:    y₂-y₁=m(X₂-X₁) .

 

5.  Call the point given (5, -3) to be (X₁,Y₁). Substitute the values into the point-slope form equation.

 

                                                            y-(-3) = -4/1 (X-5)

 

Note:  Since they want function notation, you will want to simplify this equation further.

 

6  Now solve for "Y."      y +3= -4(X-5)      To simplify use the distributive property:  For example,  a(x-b)=  a*x-a*b .      

 

7.  Subtract 3 from both sides of the equation:     Y= -4X +20 -3        y=  -4X+ 17

 

 

8.  Write it in function notation as such, f(X)=y , so  f(X)= -4X+17.        Answer