what is the standard form of the equation of the through the given point with the given slope? 1. through: (1, 2), slope =7 2. through: (3, -1), slope=-1

Question

Need a little help to completely understanding slope problems and related slope equations.

Answer 1

Here's a way to think of this.  Let our point be (a,b), and our slope be m. 

 

Imagine a point (x,y) on the line.  The slope of a line is the rise over run between two points on the line.  But we have two points: (a,b) and (x,y) are both on the line.  Well then, (y-b) is a rise, and (x-a) is a run. 

 

So m = (y-b) / (x-a).

 

That looks terrible.  Much better to multiply both sides by (x-a):

 

m (x-a) = y-b

 

y-b = m(x-a).

 

So that's our formula.  For your first problem, (a,b) = (1,2), and m = 7.  So we substitute in:

 

y-b = m(x-a)

 

y-2 = 7 (x - 1)

 

For your second problem, (a,b) = (3, -1) and m = -1.  I hope you'll forgive me if I let you do this one.

 

Cheers,

Mike N.