find an equation of the line. Write the equation using function notation. through (5,-9) and is perpendicular to 3y=x-6

Question

Please show me how to do this one.  Kind of confused.

Thanks!!

Answer 1

First of all we know that slop intercept form is:

y=mx+b

m= slope

b = y intercept.

 

we need to change the line 3y=x-6 to slope intercept form. 

3y = x-6

y = (x-6)/3       divide both sides by 3

y = (1/3)x -2    distribute

And we can see the m = 1/3

 

A perpendicular line has a slope that is the negative reciprocal.  We have to invert the fraction and make it negative, so our new slope is:

m = -3/1 = -3

 

We have been given the (x,y) coordinate (5,-9) for the new line.  This means that we know:

m = -3

x = 5

y = -9

 

We can plug these into the slope intercept equation and solve for b.

-9 = (-3)*(5) + b

-9 = -15 + b

6 = b                 add 15 to both sides

 

Now we know m=-3 and b=6 so

y=-3x+6