Partial relation

Finding the rule for partial from a table of values X 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) x1y1 x2y2 a = 6-5 2-1 a = 1

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

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

Step 1- find “a’” ( 30,560) (40,680) x1 y1 x2 y2 a = 680-560 40-30 a = 120 10 a = 12

Step 2- find the “b” pick a coordinate (30,560) x y Y = ax + b 560 = 12(30) + b 560 = 360 + b 560 – 360 = 240 + b -360 b = 200 Write the rule y = 12x + 200

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

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

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

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 – 8 d) Y = -6x +58 b) Y = -3x +17 e) Y = 0.5x -1 c) Y = -2x +4

(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