Expert: Paul Klarreich - 3/25/2008

Question
Dear Mr. Paul Klarreich,

What is the slope of the line 2x + 5y = 10 ?

Thanks so much for your time & expertise,

Celine :)

Answer
Questioner:   Celine
Category:  Advanced Math
Private:  No
 
Subject:  Slope of the Line
Question:  Dear Mr. Paul Klarreich,

What is the slope of the line 2x + 5y = 10 ?

Thanks so much for your time & expertise,

Celine :)
.....................................
Hi, Celine,

Most of this is simply pattern-matching.  You were taught this:

Slope-intercept form:

y = mx + b.

A form is a pattern.  You match a pattern to an example.

2x + 5y = 10  does not match in this form, so you work it a bit:

You need LHS = y and nothing else:

2x + 5y = 10
-2x       -2x      << Subtract.
----------------
5y = -2x + 10
5y = -2x + 10
--   ---  ---   << divide
5     5     5

y = (-2/5)x + 2  << Ready to match the pattern.

In the pattern, m is the coefficient of x.
In the example, -2/5 is the coefficient of x.

-2/5 matches m

In the pattern, m is the slope.
-2/5 matches m
-2/5 is the slope.