Find an equation of the line. Write the equation using function notation. Through (3, -6)​; perpendicular to 9y=x-18

Question

 Find an equation of the line. Write the equation using function notation. Through (3, -6); perpendicular to 9y=x-18

 

The equation of the line is: f(x)=

Answer 1

First, let's simplify the equation 9y=x-18 by dividing both sides by 9.

We end up with y=x/9-2

 

If two lines are perpendicular to each other, their slopes have a special relationship. If one of the lines have slope m, then the slope of the other line is -1/m (i.e., inverse reciprocal).

 

The slope of the equation that we simplified above is 1/9. Therefore, according to the relationship the slope of the line that is perpendicular to it must be -1/(1/9)=-9.

 

Now, we know the slope of the line. We also know a point where the line passes through, (3,-6). The rest is a trivial task.

 

y = mx+b

 

-6 = -9*(3) + b

 

b=21

 

Then, the equation of the line is y=-9x+21