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Section 3.2
Equations of Lines:
•
Standard Form: Ax + By = C where A, B, and C are numbers
o 2x + 3y = 6 is a linear equation in standard form
o x = 6 is a linear equation in standard form (B = 0)
o y = 0 is a linear equation in standard form (A = 0)
•
Slope-intercept form: y = mx + b
o m is the slope of the line
o b is the y-intercept (where it crosses the y-axis)
o y = 3x + 2
slope is 3/1 and y-intercept is (0, 2)
“Rearranging the furniture”:
•
To go from standard form to slope intercept form:
2x + 3y = 6
3y = − 2x + 6
3y = − 2x + 6
2
y=
− x+2
3
•
Hop and swap the 2x to the other side
It changes its sign and goes after the =
Now divide by 3 to get y alone
Now it’s in slope-intercept form
To go from slope-intercept form to standard form:
5
x−2
6
6y = 5x – 12
–5 x + 6y = – 12
5 x – 6y = 12
=
y
Multiply everything by 6 (LCD)
Hop and swap the 5x to the other side
Be sure that the x-term goes first
Make the x-term positive
“If you don’t like a sign, change them all”
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