1. Converting Linear Equations into Different Forms: Slope-Intercept Form and Standard Form

2. Slope intercept form is:
y = mx + b
m is slope
b is y-intercept
x is input
y is output

3. Ax + By = C Standard form is:
A (the leading coefficient) must be positive
A, B and C must be integers
A, B and C will be numbers
x and y are the variables
ie. 7x – 6y = 12
Not -3x + 9y = 4 why not?
Not 15x + 4.5y = why not?

4. Convert Into Slope-Intercept Form
(divide both sides by 2 to get y alone)
(now simplify all fractions) 2 1

5. Convert From Standard Form Into Slope-Intercept Form
21x – 7y =14
(subtract 21x from both sides)
(now divide both sides by -7)
-7y = -21x + 14
(simplify all fractions)
y = 3x – 2

6. Convert From Standard Form Into Slope-Intercept Form
4x+3y=24
-4x
-4x
3y=-4x+24 3 3 3

7. Convert From Slope-Intercept Form Into Standard Form
y = -1/3x + 7
(put in Ax + By = C)
+1/3x +1/3x
(add 1/3x to both sides)
Standard form must have a positive leading coefficient (A)
and A, B, and C must be integers, so clear out the fractions by multiplying every term by 3
1/3x + y = 7
x + 3y = 21

8. Convert From Slope-Intercept Form Into Standard Form
y = 2.5x + 1
(subtract 2.5x from both sides)
-2.5x x
Standard form must have a positive leading coefficient (A)
and A, B, and C must be integers, so clear out the negative decimal by multiplying every term by -2
-2.5x + y = 1
5x - 2y = -2

9. Convert to Slope-Intercept Form:
5y = x
(divide both sides by 5 to get y alone)
5y = x
5y = x
(now simplify all fractions)
(write in y=mx+b order)
y = 2x + 3

10. Convert Into Slope-Intercept Form
2y + 26 = -6x
(subtract both sides by 26)
(now divide both sides by 2
2y = -6x - 26
(simplify all fractions)
y = -3x - 13

11. Convert Into Slope-Intercept Form
2x = 5y - 10
2x = 5y-10 -5y -5y
2x – 5y = x x
-5y = -2x –
y = 2/5x + 2