1. Partial relation

2. Finding the rule for partial from a table of valuesX 1 2 4 6 y 5 8 10
Remember: the rule “looks” like y = ax + b
Step 1: find the rate of change
(1,5) (2,6)
x1y x2y2
a = 6-5
2-1
a = 1

3. Step 2: find the initial value “b”
y = ax + b
you need to pick 1 of the coordinates
to substitute into the rule (1,5)
x,y
5 = 1(1) + b
5 = 1 + b
5 – 1 = 1 + b - 1
4 = b now put it back into the rule

4. So far you have a = 1 and b = 4 that’s all you need to do this !!!
Rule y = 1x + 4
Try the following example..follow the pattern X 30 40 y
560
680

5. Step 1- find “a’”
( 30,560) (40,680)
x1 y x2 y2
a =
40-30
a = 120 10
a = 12

6. Step 2- find the “b”
pick a coordinate (30,560)
x y
Y = ax + b
560 = 12(30) + b
560 = b
560 – 360 = b -360
b = 200
Write the rule y = 12x + 200

7. Find the rule for these partial relations
1- ( 3,15) and (-2,-5)
2- (2,2) and (-5,23)
3- (6,38) and (11,53)
Follow all the steps like in your notes.
Answers
1- y=4x+3
2- y=-3x +8
3- y=3x +20

8. How to find the rule for partial from a graph
On the graph look to see if the line passes through the y-axis at point that you know.
in this case you know
that the b=3.
Pick the coordinates of the initial value (0,3) and then 1 other point. Use these 2 points to calculate “a”.
Once you have calculated “a” you can write out the rule in the form of y=ax+b 3

9. How to find the rule for partial when you don’t know B
On the graph, pick two points that are definitely on the line.
Find the rate of change
Follow the steps for finding the rule for partial based on a table of values

10. Practice equation of a line
Write the equation of the line that passes through the following points.
Be sure to show all work required…neatly.
(3,-2) and (4,0) b) (7,-4) and (4,5)
(1,2) and (3,-2) d) (9,4) and (10,-2)
e) (4,1) (12,5)
Answers
a) Y = 2x – d) Y = -6x +58
b) Y = -3x e) Y = 0.5x -1
c) Y = -2x +4

11. (3,-2) ( 4,0)
x1y 1 x2 y2
Find “a”= 0 – (-2)
4-3
a = 2 1
Find “b” y = ax + b
0 = 2(4) +b
0 = 8 + b
0-8 = 8 + b – 8
-8 = b
Write the rule y = ax + b
y = 2x - 8