## Tuesday, March 04, 2008

### linear equations

Few people will appreciate this rant, but here it is anyway:

The Algebra 1 textbook I use introduces equations of lines in 'standard' form, which I find generally useless, but okay. Then it introduces slope-intercept form when you're given the slope and the intercept, makes sense, but its rather unnecessary because point-slope works perfectly here. The next section is all about how to get a slope-intercept equation when you are given a slope and a non-intercept point. Why would you ever do this if you have point-slope form? I understand if slope-intercept were really intuitive, but point-slope is the intuitive one, it comes directly from the definition of slope. So finally, they introduce point-slope, but the section focuses entirely on converting it into slope-intercept or standard form! There isn't a single problem in the section which has them write an equation from two points or from a graph. Seriously, why??

I am very curious who fell in love with y=mx + b and spread it throughout the math world.

Reference for those who haven't taken Algebra 1 in a while:

Standard Form: Ax + By = C
A, B, C whole #'s (meaningless on their own)

Slope-Intercept: y = mx + b
m = slope, b = y-intercept

Point-Slope: y - y1 = m(x - x1)
m = slope, (x1, y1) = any point on the line

The average problem in the real world gives you two points or a point and slope. Rarely is that point the y-intercept. Standard Form is good for lemonade/ice tea stands, that's about it.