Find an equation of a line

Question

Find an equation of the line. Write the equation using function notation. (Show all work)

 

Through (2,-5);perpendicular to 9y=x-18

Answer 1

Hi Again Theresa;

Another great question!

(2,-5)

9y=x-18

Our first priority is to place this formula into the format of...

y=mx+b

The y must be completely isolated.

So...

9y=x-18

We will divide both sides by 9...

9y/9=(x/9)-(18/9)

y=(x/9)-2

The slope is 1/9.

The slope of the perpendicular line is -9.

The y-intercept, the value of b when x=0, may or may not be -2.

y=-9x+b

Let's plug-in the provided coordinate of (2,-5)...

-5=-9(2)+b

-5=-18+b

If we add 18 to both sides...

13=b

y=-9x+13

 

Answer 2

9y=x-18

put the equation in the slope-intercept form: y=mx+b

9y/9=x/9-18/9

y=(1/9)x-2

if two lines are perpendicular to each other, they have slopes that are negative reciprocals of each other

the slope of the perpendicular line is -9

now we have y=-9x+b

using (2,-5), we have -5=-9(2)+b

-5=-18+b and b=13

answer: y=-9x+13

using point-slope form, we have y-(-5)=-9(x-2)

y+5=-9x+18

y=-9x+13