1. FINDING THE EQUATION OF A LINE
KNOWN SITUATIONS:
SLOPE & Y INTERCEPT
SLOPE & 1 POINT
TWO POINTS
TRANSLATION

2. SLOPE & Y INTERCEPT HOW TO FIND EQUATION OF A LINE IF:
You have SLOPE (a) and Y INTERCEPT (b)
METHOD: SUBSTITUTE BOTH (a) and (b) in the equation.
EXAMPLE: SLOPE is and Y INTERCEPT is -1.
y = 2 3 x - 1

3. SLOPE & 1 POINT HOW TO FIND EQUATION OF A LINE IF:
You have SLOPE (a) and a POINT (x, y)
METHOD: SUBSTITUTE for (a) and (x, y) in the equation.
EXAMPLE: SLOPE is 2 and POINT is (3, 5)
y = ax + b turns to
5 = 2(3) + b find for b
5 – 6 = b b = -1 therefore
y = 2x – 1

4. TWO POINTS HOW TO FIND EQUATION OF A LINE IF:
You have TWO POINTS (x1, y1) and (x2, y2)
METHOD: PART A – FIND THE SLOPE
PART B – SUBSTITUTE ONE OF THE POINTS + SLOPE
(as in example 2)
EXAMPLE: (1, 3) and (4, -6)
a = y2 −y1 x2 −x1 = −6 −3 4 −1 = −9 3 = - 3

5. TWO POINTS SLOPE is – 3, then take one point (1, 3) or (4, -6)
y = ax +b
3 = -3(1) + b then find for b
3 + 3 = b b = 6 therefore
y = -3x + 6

6. TRANSLATION GENERAL STANDARD SLOPE
Ax + By + C = 0 Ax + By = C y = Ax + B
Any time you translate General form or
Standard form to Slope form make sure you find for y (singular)
Any time you translate General form to Standard form make sure you switch symbols for C as you send C to the other side of the = sign

7. TRANSLATION GENERAL FORM to SLOPE FORM
3x + 2y + 4 = 0 step 1 = isolate y
2y = -3x – 4 step 2 = find for y
y = x – 2
SLOPE FORM TO GENERAL FORM
y = x – 2 step 1= bring to one side
3 2 x +y + 2 = 0 step 2 = eliminate fractions
3x + 2y + 4 = 0

8. TRANSLATION STANDARD FORM to SLOPE FORM
2x + 3y = -2 step 1 = isolate y
3y = -2x – 2 step 2 = find for y
y = x – 2 3
SLOPE FORM to STANDARD FORM
y = x – step 1 = bring x & y to
2 3 x + y = one side
2x + 3y = -2 step 2 = eliminate fraction