Expert: Steve Holleran - 9/3/2008

Question
Hi I am stuck on a particular problem. The question is using line 1: x+5y=10, Find an equation to the line that passes through (-3, 5) and is parallel to line 1. Well I know in order for them to be parallel their slopes must be the same. I calculated the slope at 1/5. I am not quite sure where to go from here. I had down the next step would be "  y-5=1/5(x+3), but I am not sure if this is correct and I am not sure what steps to take next or how to take an equation of the line and put it into an ax+by=c  formula.
Thanks.

Answer
Hi Stephanie,

Okay, the line you have is x + 5y = 10

Solving for y, we get          5y = -x + 10

so                              y = -1/5 x + 2  and the slope of

Line 1 is m = -1/5.

You are correct that the slopes of parallel lines must be equal, so the slope of the line you're looking for is also -1/5:

                    y = -1/5 x + b

Now, since the second line has to pass through (-3, 5), substitute these coordinates in for x and y in the equation, and that will determine b:

                    5 = -1/5 * -3 + b

                    5 = 3/5 + b   so b = 5 - 3/5 = 4 2/5 = 22/5

so your equation is

                        y = (-1/5)x + 22/5

You can change this to standard form if you want by multiplying by 5:

                     5y = -1x + 22

                    x + 5y = 22


Hope this helps
Steve