Equation of the Line

[mathdad]

What is the equation for y if it passes through (0,0) and (c,d)?

Solution:

Let m = slope

m = (d - 0)/(c - 0)

m = d/c

y - y_1 = m(x - x_1)

I will use (0, 0).

y - 0 = d/c(x - 0)

y = (d/c)x

What if I use the other point?

y - d = (d/c)(x - c)

y - d = (d/c)x - (d/c)c

y - d = (d/c)x - d

y = (d/c) - d + d

y = (d/c)x

It works either way. What do you say?

 

[Romsek]

it will work using any point on the line

 

[Steven G]

It better work using either point.

 

[mathdad]

Wonderful. Another one for the files.

 

[HallsofIvy]

Another way to do this: any non-vertical line can be written as y= ax+ b for some numbers a and b. If the line goes through (0, 0) then 0= a(0)+ b so b= 0. If the line also goes through (c, d) then d= a(c)+ 0 so a= d/c. y= (d/c)x.

 

[mathdad]

Thank you everyone. Look for my new set of distance word problems.