Expert: Chanda Walker - 1/4/2009

Question
i know that in finding the slope you use the "y-y/x-x" with the subscripts and all. but isnt there another formula for slope, something like "-x/y"? i have the following problem:

"the equation of the line parallel to 2x-5y=-2 and containing the point (3,-4) is..." and it lists 4 choices. should i use "y=mx+b" or something else?

Answer
Allison you are SO close to having it perfect.

Your formula for the slope of the line is right
m = (y_2 -y_1)/(x_2 - x_1)

The formula you list as -x/y is the slope of the line perpendicular to that.  More formally it would be written as

-(x_2 - x_1)/(y_2 - y_1)

The definition of parallel lines is that two lines are parallel when their slopes are equal.

You need to rewrite the equation you were given in the form y = mx + b:

y = 2/5 x + 2/5

The slope of both lines (since they are parallel) is 2/5.

To complete the equation, since you know the slope, all you need is the intercept, b.

Just take the coordinates given, (3, -4) and put them into the equation you know so far and solve for b.

y = 2/5 x + b
-4 = (2/5)* 3 + b
b = -4 - 6/5
b = -26/5


Your new parallel line is:

y = (2/5) x - 26/5

Thanks for the question.  Please don't forget to rate this answer.