Partial relation

Partial variation relation I received a flyer in the mail from a landscaping company that maintains lawns in my area. They charge $5 for the use of their equipment and then $4 per hour to cut and trim the grass. Independent variable: # of hours it takes Dependent variable: the amount I must pay $ Rate of Change: $4 per hour

Table of values Number of hours 1 2 4 Cost $ 5 9 13 21 The table of values will have a “initial value or starting cost”. This is the value of y when x=0 In our situation, the initial value is = to 5 The initial value has a symbol “b” The table of values is NOT PROPORTIONAL…means you cannot cross multiply to get the same answer.

Graph The line of the graph does not go through the origin. The line starts above or below the origin The line starts at the initial value “b” and then goes in a straight line.

graph • Initial value is where the line crosses the y axis Number of hours Cost 1 2 3 4 22 - 20 - 18 - 16 - 14 - 12 - 10 - 8 - 6 - 4 - 2 - (4,21) (2,13) (1,9) • Initial value is where the line crosses the y axis The initial value is also called the y-intercept

y = 4x + 5 y = 5 + 4x y = ax + b rule Rule for our situation rule looks like this: y = ax + b dep = (r.o.c)(indep var) + initial value Rule for our situation y = 4x + 5 y = 5 + 4x

Work to do 4306 Workbook Page 110-11 activity 4 Page 117 #10 and #11 Textbook #2 direct and partial questions Direct: page 102 #4,5 103 #6,7 Partial page 117 #4..find r.o.c. and then write the rule y=ax +b

Work to do…..306-05 Workbook is your HOMEWORK Page 117 #10 and #11 Textbook #2 IS NOT HOMEWORK page 117 #4..step 1 find r.o.c. “a” step 2 find initial value “b” step 3 write the rule y=ax +b

Work to do -92’s & 91’s Workbook Textbook #2 Page 117 #10 and #11 Page 115 #1 a-h page 117 #4a-e..step 1 find r.o.c. “a” step 2 find initial value “b” step 3 write the rule y=ax +b

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 Textbook #2 page 115 #1a-h Find ‘a’ and ‘b’ and then write the rule in form of y=ax+b

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

Work 4306 + 91’s Workbook homework Page 121 #3-7 Not for homework but work on it if you finish the above Page 112 #1,2 Page 113 #3,4,5 Page 114#5,6

92’s Workbook homework Page 121 #3-7 Page 112 #1,2 Page 113 #3,4,5(use -1,0,1 as x values in the table of values) Page 114#5 continued

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) Y = 2x – 8 Y = -3x +17 Y = -2x +4 Y = -6x +58 e) (4,1) (12,5) Y = 0.5x -1

(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

Homework 4306 Finish the 5 questions (finding equation or rule) Textbook #2 page 119 #13 page 120 #16 page 125 #32 Expect an assessment on finding the rule on Wednesday or Thursday

91’s workbook Page 112 #1,2 Page 113 #3,4,5 Page 114#5 continued #6 Textbook #2 page 119 #13 page 120 #16 page 125 #32 Mini assessment this week on finding the equation of the line.