Math CC 78 Be Prepared On Desk Labsheet
Math CC 7/8 – Be Prepared On Desk: Labsheet 1. 3 Moving Straight Ahead (MSA) In Your Journal: 1) Add to your vocabulary: (We will review. ) Linear Relationship Y-intercept Slope Coefficient 2) Glue in yesterday’s WS 3) Date & Title: MSA 1. 3 Using Linear Relationships In Your Planner: 1. HW: MSA p. 18 #6, 8, 24 2. AN, SD, SS Final Retake-Thurs. Nov. 29 th After School 3. CS Retake-Mon. Dec. 3 rd
Tasks for Today • Wrap Up lesson 1. 2 • Lesson 1. 3 • Pass back CS Test – Go over
* Table * Graph * Equation
The greater the walking rate, the steeper the line on the graph. (or greater slope) What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6, 12) represent? Whose line is it on? Whose line are these points on? (9, 9) (5, 12)
Labsheet 1. 2 from yesterday! The walking rate is Alana: d = t or y = 1 x + 0 or y = x represented as the number Gilberto: d = 2 t or y = 2 x + 0 or y = 2 x that time is multiplied by Leanne: d = 2. 5 t or y = 2. 5 x + 0 or y = 2. 5 x to get the distance. This is the number in front of the variable. It is called the coefficient.
In the table, for every increase of 1 unit in x, the value of y increases by a constant amount. Each equation is of the form y = mx Which represents a proportional relationship. The graph of a proportional relationship is a straight line that passes through the origin.
All three relationships between distance walked and time are proportional. They are all of the form d = rt The value of r is the constant of proportionality for each relationship. (slope) (unit rate!)
Alana: increases by 1 m Alana: d = t or y = 1 x + 0 or d=1(1) Gilberto: increases by 2 m Gilberto: d = 2 t or y = 2 x + 0 or d=2(1) Leanne: increases by 2. 5 m Leanne: d = 2. 5 t or y = 2. 5 x + 0 or d=2. 5(1) In the table it is found as the difference between the values for distance. In the graph it is the steepness of the line. As x increases by 1, y goes up 1 for Alana, 2 for Gilberto, and 2. 5 for Leanne.
If t increases by 5 seconds: Increases by 5 meters Alana: d = t or d=1(5) ( y = 1 x + 0 ) ( y = 2 x + 0 ) Increases by 10 meters Gilberto: d = 2 t or d=2(5) Increases by 12. 5 meters. Leanne: d = 2. 5 t or d=2. 5(5) ( y = 2. 5 x + 0 ) In a table – As x increases by 5, find the difference in y values. In a graph – the difference in y-coordinates of two points on the line whose difference in x-coordinates is 5.
Walking rates per minute: Walking rates per hour: Alana: 60 m/min Gilberto: 120 m/min Leanne: 150 m/min Alana: 3, 600 m/hr Gilberto: 7, 200 m/hr Leanne: 9, 000 m/hr (walking rate per sec x 60 sec) (walking rate per min x 60 min)
George = No Elizabeth = Yes! Constant rate 3 m/2 s Billie = Yes! Constant rate 2. 25 m/s Bob = No
Who will raise the most money after d kilometers? Labsheet 1. 3
Independent What is the starting point for each student? This is also called the y-intercept. What is the rate of change for each student? This is also called the slope. Variable Distance = X Dependent Variable $=Y
What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6, 12) represent? Whose line is it on? Whose line are these points on? (10, 10) (6, 8)
Leanne: y = 0 x + 10 or y = 10 y = money earned in dollars Gilberto: y = 2 x or y = 2 x + 0 The coefficient (the number in front of the variable) represents the walking rate. Alana: y = 0. 50 x + 5 x = distance walked in km
Alana: as (x) increases by 1 km, (y) increases by $0. 50 Gilberto: as (x) increases by 1 km, (y) increases by $2 Leanne: as (x) increases by 1 km, (y) has no change Graph: show pattern on graph… Equation: the pattern of change is the coefficient of x Leanne: y = 0 x + 10 Gilberto: y = 2 x Alana: y = 0. 50 x + 5
Add to Journal: In a table: as x increases by 1, y changes by a constant amount In a graph: there is a straight line In an equation: it follows the form of y = mx + b The relationship between money and distance walked for… Gilberto IS proportional! It is NOT proportional for Leanne and Alana because sponsors donate an initial amount in addition to money donated per kilometer. This makes the ratio of money donated to kilometers walked not a constant.
Alana: $5 + 0. 5(8) = $9 Gilberto: $2 x 8 km = $16 Leanne: $10 per sponsor no matter how far she walks Alana: $5 + 0. 5(? ) = $10, so 0. 5 x 10 km = 5 Gilberto: $2 x ? km = $10, so 10/2 = 5 km Leanne: Can’t determine!
(12, 11) lies on Alana’s graph. If Alana walks 12 km, each sponsor donates $11. When her distance is zero, she already has $5 (0, 5) it is the starting point, or y-intercept! 5 is the term added to 0. 5 x Alana: y = 0. 50 x + 5
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