Question

Find an equation of the line parallel to x=5y-9 and passing through (2,-4). Express in standard form.

Answer 1

Answer:

x - 5y = 22

Step-by-step explanation:

Step 1:  rewrite the equation of the given line in to slope-intercept form by solving for y

 x = 5y - 9    

     -5y = -x - 9               (subtract 5y and x from both sides)

        y = x/5 + 9/5           (divide both side by -5)

Step 2:  Our line is parallel to this line, so it has the same slope, but a different  y-intercept, so set up the equation...

  y = x/5 + b      

We are given a  point (x, y) of (2, -4), so plug that in and solve for b.  

 -4 = 2/5 + b

            -4 - 2/5 = b      (subtract 2/5 from both sides to isolate b)  

                   -20/5 - 2/5 = b

 

                         -22/5 = b      (simplify)

So the equation of our line is  y = x/5 - 22/5

Step 3:  Standard form is ax + by = c, where a is a positive integer

subtract x/5 from both sides...

-x/5 + y = - 22/5

multiply by -5 so x becomes a positive integer

x - 5y = 22